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  • Homology Groups of Cubical Sets with Connections
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2021-01-08
    Hélène Barcelo, Curtis Greene, Abdul Salam Jarrah, Volkmar Welker

    Toward defining commutative cubes in all dimensions, Brown and Spencer introduced the notion of “connection” as a new kind of degeneracy. In this paper, for a cubical set with connections, we show that the connections generate an acyclic subcomplex of the chain complex of the cubical set. In particular, our results show that the homology groups of a cubical set with connections are independent of whether

    更新日期:2021-01-08
  • A Categorical Approach to Linkage
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2021-01-07
    Alexander York

    Linkage of ideals is a very well-studied topic in algebra. It has lead to the development of module linkage which looks to extend the ideas and results of the former. Although linkage has been used extensively to find many interesting and impactful results, it has only been extended to schemes and modules. This paper builds a framework in which to perform linkage from a categorical perspective. This

    更新日期:2021-01-07
  • The Grothendieck Group of an n -exangulated Category
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2021-01-06
    Johanne Haugland

    We define the Grothendieck group of an n-exangulated category. For n odd, we show that this group shares many properties with the Grothendieck group of an exact or a triangulated category. In particular, we classify dense complete subcategories of an n-exangulated category with an n-(co)generator in terms of subgroups of the Grothendieck group. This unifies and extends results of Thomason, Bergh–Thaule

    更新日期:2021-01-07
  • Vector Bundles and Differential Bundles in the Category of Smooth Manifolds
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2021-01-02
    Benjamin MacAdam

    A tangent category is a category equipped with an endofunctor that satisfies certain axioms which capture the abstract properties of the tangent bundle functor from classical differential geometry. Cockett and Cruttwell introduced differential bundles in 2017 as an algebraic alternative to vector bundles in an arbitrary tangent category. In this paper, we prove that differential bundles in the category

    更新日期:2021-01-02
  • Monoid Properties as Invariants of Toposes of Monoid Actions
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-12-03
    Jens Hemelaer, Morgan Rogers

    We systematically investigate, for a monoid M, how topos-theoretic properties of \({{\,\mathrm{\mathbf {PSh}}\,}}(M)\), including the properties of being atomic, strongly compact, local, totally connected or cohesive, correspond to semigroup-theoretic properties of M.

    更新日期:2020-12-03
  • The Chromatic Brauer Category and Its Linear Representations
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-12-02
    L. Felipe Müller, Dominik J. Wrazidlo

    The Brauer category is a symmetric strict monoidal category that arises as a (horizontal) categorification of the Brauer algebras in the context of Banagl’s framework of positive topological field theories (TFTs). We introduce the chromatic Brauer category as an enrichment of the Brauer category in which the morphisms are component-wise labeled. Linear representations of the (chromatic) Brauer category

    更新日期:2020-12-02
  • Morphisms of Rational Motivic Homotopy Types
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-11-19
    Ishai Dan-Cohen, Tomer Schlank

    We investigate several interrelated foundational questions pertaining to the study of motivic dga’s of Dan-Cohen and Schlank (Rational motivic path spaces and Kim’s relative unipotent section conjecture. arXiv:1703.10776) and Iwanari (Motivic rational homotopy type. arXiv:1707.04070). In particular, we note that morphisms of motivic dga’s can reasonably be thought of as a nonabelian analog of motivic

    更新日期:2020-11-19
  • On Equalizers in the Category of Locales
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-11-19
    Jorge Picado, Aleš Pultr

    The fact that equalizers in the context of strongly Hausdorff locales (similarly like those in classical spaces) are closed is a special case of a standard categorical fact connecting diagonals with general equalizers. In this paper we analyze this and related phenomena in the category of locales. Here the mechanism of pullbacks connecting equalizers is based on natural preimages that preserve a number

    更新日期:2020-11-19
  • Discrete and Conservative Factorizations in Fib ( B )
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-11-04
    Alan S. Cigoli, Sandra Mantovani, Giuseppe Metere

    We focus on the transfer of some known orthogonal factorization systems from \(\mathsf {Cat}\) to the 2-category \({\mathsf {Fib}}(B)\) of fibrations over a fixed base category B: the internal version of the comprehensive factorization, and the factorization systems given by (sequence of coidentifiers, discrete morphism) and (sequence of coinverters, conservative morphism) respectively. For the class

    更新日期:2020-11-04
  • Codenseness and Openness with Respect to an Interior Operator
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-10-26
    Fikreyohans Solomon Assfaw, David Holgate

    Working in an arbitrary category endowed with a fixed \(({\mathcal {E}}, {\mathcal {M}})\)-factorization system such that \({\mathcal {M}}\) is a fixed class of monomorphisms, we first define and study a concept of codense morphisms with respect to a given categorical interior operator i. Some basic properties of these morphisms are discussed. In particular, it is shown that i-codenseness is preserved

    更新日期:2020-10-30
  • The Homotopy Category of Cotorsion Flat Modules
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-10-24
    Hossein Eshraghi, Ali Hajizamani

    This paper aims at studying the homotopy category of cotorsion flat left modules \({{\mathbb {K}}({\mathrm{CotF}}\text {-}R)}\) over a ring R. We prove that if R is right coherent, then the homotopy category \({\mathbb {K}}(\mathrm{dg}\text {-}\mathrm{CotF}\text {-}R)\) of dg-cotorsion complexes of flat R-modules is compactly generated. This uses firstly the existence of cotorsion flat preenvelopes

    更新日期:2020-10-30
  • A Constructive Approach to Freyd Categories
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-10-13
    Sebastian Posur

    We discuss Peter Freyd’s universal way of equipping an additive category \(\mathbf {P}\) with cokernels from a constructive point of view. The so-called Freyd category \(\mathcal {A}(\mathbf {P})\) is abelian if and only if \(\mathbf {P}\) has weak kernels. Moreover, \(\mathcal {A}(\mathbf {P})\) has decidable equality for morphisms if and only if we have an algorithm for solving linear systems \(X

    更新日期:2020-10-13
  • Gabriel–Zisman Cohomology and Spectral Sequences
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-10-10
    Imma Gálvez-Carrillo, Frank Neumann, Andrew Tonks

    Extending constructions by Gabriel and Zisman, we develop a functorial framework for the cohomology and homology of simplicial sets with very general coefficient systems given by functors on simplex categories into abelian categories. Furthermore we construct Leray type spectral sequences for any map of simplicial sets. We also show that these constructions generalise and unify the various existing

    更新日期:2020-10-11
  • The Kechris–Pestov–Todorčević Correspondence from the Point of View of Category Theory
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-09-28
    Dragan Mašulović

    The Kechris–Pestov–Todorčević correspondence (KPT-correspondence for short) is a surprising correspondence between model theory, combinatorics and topological dynamics. In this paper we present a categorical re-interpretation of (a part of) the KPT-correspondence with the aim of proving a dual statement. Our strategy is to take a “direct” result and then analyze the necessary infrastructure that makes

    更新日期:2020-09-28
  • Exponential Functions in Cartesian Differential Categories
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-09-24
    Jean-Simon Pacaud Lemay

    In this paper, we introduce differential exponential maps in Cartesian differential categories, which generalizes the exponential function \(e^x\) from classical differential calculus. A differential exponential map is an endomorphism which is compatible with the differential combinator in such a way that generalizations of \(e^0 = 1\), \(e^{x+y} = e^x e^y\), and \(\frac{\partial e^x}{\partial x} =

    更新日期:2020-09-25
  • Different Exact Structures on the Monomorphism Categories
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-09-02
    Rasool Hafezi, Intan Muchtadi-Alamsyah

    Let \({\mathcal {X}}\) be a contravariantly finite resolving subcategory of \({\mathrm{{mod\text{- }}}}\varLambda \), the category of finitely generated right \(\varLambda \)-modules. We associate to \({\mathcal {X}}\) the subcategory \({\mathcal {S}}_{{\mathcal {X}}}(\varLambda )\) of the morphism category \(\mathrm{H}(\varLambda )\) consisting of all monomorphisms \((A{\mathop {\rightarrow }\limits

    更新日期:2020-09-02
  • On the Axiomatisability of the Dual of Compact Ordered Spaces
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-08-20
    Marco Abbadini, Luca Reggio

    We provide a direct and elementary proof of the fact that the category of Nachbin’s compact ordered spaces is dually equivalent to an \(\aleph _1\)-ary variety of algebras. Further, we show that \(\aleph _1\) is a sharp bound: compact ordered spaces are not dually equivalent to any \(\mathrm{SP}\)-class of finitary algebras.

    更新日期:2020-08-20
  • Gabriel–Ulmer Duality for Topoi and its Relation with Site Presentations
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-08-20
    Ivan Di Liberti, Julia Ramos González

    Let \(\kappa \) be a regular cardinal. We study Gabriel–Ulmer duality when one restricts the 2-category of locally \(\kappa \)-presentable categories with \(\kappa \)-accessible right adjoints to its locally full sub-2-category of \(\kappa \)-presentable Grothendieck topoi with geometric \(\kappa \)-accessible morphisms. In particular, we provide a full understanding of the locally full sub-2-category

    更新日期:2020-08-20
  • Crossed Modules of Monoids III. Simplicial Monoids of Moore Length 1
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-08-20
    Gabriella Böhm

    This is the last part of a series of three strongly related papers in which three equivalent structures are studied: Internal categories in categories of monoids; defined in terms of pullbacks relative to a chosen class of spans Crossed modules of monoids relative to this class of spans Simplicial monoids of so-called Moore length 1 relative to this class of spans. The most important examples of monoids

    更新日期:2020-08-20
  • The Category of Factorization
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-08-17
    Brandon Goodell, Sean K. Sather-Wagstaff

    We introduce and investigate the category of factorization of a multiplicative, commutative, cancellative, pre-ordered monoid A, which we denote \(\mathcal {F}(A)\). The objects of \(\mathcal {F}(A)\) are factorizations of elements of A, and the morphisms in \(\mathcal {F}(A)\) encode combinatorial similarities and differences between the factorizations. We pay particular attention to the divisibility

    更新日期:2020-08-17
  • Raney Algebras and Duality for $$T_0$$ T 0 -Spaces
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-08-09
    G. Bezhanishvili, J. Harding

    In this note we adapt the treatment of topological spaces via Kuratowski closure and interior operators on powersets to the setting of \(T_0\)-spaces. A Raney lattice is a complete completely distributive lattice that is generated by its completely join prime elements. A Raney algebra is a Raney lattice with an interior operator whose fixpoints completely generate the lattice. It is shown that there

    更新日期:2020-08-09
  • Exact and Strongly Exact Filters
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-07-25
    M. A. Moshier, A. Pultr, A. L. Suarez

    A meet in a frame is exact if it join-distributes with every element, it is strongly exact if it is preserved by every frame homomorphism. Hence, finite meets are (strongly) exact which leads to the concept of an exact resp. strongly exact filter, a filter closed under exact resp. strongly exact meets. It is known that the exact filters constitute a frame \({\mathrm{Filt}}_{{\textsf {E}}}(L)\) somewhat

    更新日期:2020-07-25
  • The DG-Category of Secondary Cohomology Operations
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-06-23
    Hans-Joachim Baues, Martin Frankland

    We study track categories (i.e., groupoid-enriched categories) endowed with additive structure similar to that of a 1-truncated DG-category, except that composition is not assumed right linear. We show that if such a track category is right linear up to suitably coherent correction tracks, then it is weakly equivalent to a 1-truncated DG-category. This generalizes work of the first author on the strictification

    更新日期:2020-06-24
  • A Categorical Construction for the Computational Definition of Vector Spaces
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-06-23
    Alejandro Díaz-Caro; Octavio Malherbe

    Lambda-\({\mathcal {S}}\) is an extension to first-order lambda calculus unifying two approaches of non-cloning in quantum lambda-calculi. One is to forbid duplication of variables, while the other is to consider all lambda-terms as algebraic linear functions. The type system of Lambda-\({\mathcal {S}}\) has a constructor S such that a type A is considered as the base of a vector space while S(A) is

    更新日期:2020-06-23
  • A Categorical Duality for Semilattices and Lattices
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-06-11
    Sergio A. Celani; Luciano J. González

    The main aim of this article is to develop a categorical duality between the category of semilattices with homomorphisms and a category of certain topological spaces with certain morphisms. The principal tool to achieve this goal is the notion of irreducible filter. Then, we apply this dual equivalence to obtain a topological duality for the category of bounded lattices and lattice homomorphism. We

    更新日期:2020-06-11
  • The Order-Sobrification Monad
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-06-10
    Xiaodong Jia

    We investigate the so-called order-sobrification monad proposed by Ho et al. (Log Methods Comput Sci 14:1–19, 2018) for solving the Ho–Zhao problem, and show that this monad is commutative. We also show that the Eilenberg–Moore algebras of the order-sobrification monad over dcpo’s are precisely the strongly complete dcpo’s and the algebra homomorphisms are those Scott-continuous functions preserving

    更新日期:2020-06-10
  • Hausdorff Coalgebras
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-04-30
    Dirk Hofmann; Pedro Nora

    As composites of constant, finite (co)product, identity, and powerset functors, Kripke polynomial functors form a relevant class of \(\textsf {Set}\)-functors in the theory of coalgebras. The main goal of this paper is to expand the theory of limits in categories of coalgebras of Kripke polynomial functors to the context of quantale-enriched categories. To assume the role of the powerset functor we

    更新日期:2020-04-30
  • Exact Filters and Joins of Closed Sublocales
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-03-07
    R. N. Ball; M. A. Moshier; A. Pultr

    We prove, for a general frame, that the sublocales that can be represented as joins of closed ones are, somewhat surprisingly, in a natural one-to-one correspondence with the filters closed under exact meets, and explain some subfit facts from this perspective. Furthermore we discuss the filters associated in a similar vein with the fitted sublocales.

    更新日期:2020-03-07
  • A Topological Groupoid Representing the Topos of Presheaves on a Monoid
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-03-06
    Jens Hemelaer

    Butz and Moerdijk famously showed that every (Grothendieck) topos with enough points is equivalent to the category of sheaves on some topological groupoid. We give an alternative, more algebraic construction in the special case of a topos of presheaves on an arbitrary monoid. If the monoid is embeddable in a group, the resulting topological groupoid is the action groupoid for a discrete group acting

    更新日期:2020-03-06
  • Recognizing Quasi-Categorical Limits and Colimits in Homotopy Coherent Nerves
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-03-06
    Emily Riehl; Dominic Verity

    In this paper we prove that various quasi-categories whose objects are \(\infty \)-categories in a very general sense are complete: admitting limits indexed by all simplicial sets. This result and others of a similar flavor follow from a general theorem in which we characterize the data that is required to define a limit cone in a quasi-category constructed as a homotopy coherent nerve. Since all quasi-categories

    更新日期:2020-03-06
  • Universal Central Extensions of Internal Crossed Modules via the Non-abelian Tensor Product
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-03-02
    Davide di Micco; Tim Van der Linden

    In the context of internal crossed modules over a fixed base object in a given semi-abelian category, we use the non-abelian tensor product in order to prove that an object is perfect (in an appropriate sense) if and only if it admits a universal central extension. This extends results of Brown and Loday (Topology 26(3):311–335, 1987, in the case of groups) and Edalatzadeh (Appl Categ Struct 27(2):111–123

    更新日期:2020-03-02
  • Crossed Modules of Monoids II: Relative Crossed Modules
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-02-27
    Gabriella Böhm

    This is the second part of a series of three strongly related papers in which three equivalent structures are studied: Internal categories in categories of monoids; defined in terms of pullbacks relative to a chosen class of spans. Crossed modules of monoids relative to this class of spans. Simplicial monoids of so-called Moore length 1 relative to this class of spans.The most important examples of

    更新日期:2020-02-27
  • Word operads and admissible orderings
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-01-18
    Vladimir Dotsenko

    We use Giraudo’s construction of combinatorial operads from monoids to offer a conceptual explanation of the origins of Hoffbeck’s path sequences of shuffle trees, and use it to define new monomial orders of shuffle trees. One such order is utilised to exhibit a quadratic Gröbner basis of the Poisson operad.

    更新日期:2020-01-18
  • Compactly Generated Spaces and Quasi-spaces in Topology
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-01-18
    Willian Ribeiro

    The notions of compactness and Hausdorff separation for generalized enriched categories allow us, as classically done for the category \(\textsf {Top}\) of topological spaces and continuous functions, to study compactly generated spaces and quasi-spaces in this setting. Moreover, for a class \(\mathcal {C}\) of objects we generalize the notion of \(\mathcal {C}\)-generated spaces, from which we derive

    更新日期:2020-01-18
  • Abelian Categories Arising from Cluster Tilting Subcategories
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2020-01-03
    Yu Liu; Panyue Zhou

    For a triangulated category \({\mathcal {T}}\), if \({\mathcal {C}}\) is a cluster-tilting subcategory of \({\mathcal {T}}\), then the factor category \({\mathcal {T}}{/}{\mathcal {C}}\) is an abelian category. Under certain conditions, the converse also holds. This is a very important result of cluster-tilting theory, due to Koenig–Zhu and Beligiannis. Now let \({\mathcal {B}}\) be a suitable extriangulated

    更新日期:2020-01-03
  • The Gray Monoidal Product of Double Categories
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-12-18
    Gabriella Böhm

    The category of double categories and double functors is equipped with a symmetric closed monoidal structure. For any double category \({\mathbb {A}}\), the corresponding internal hom functor sends a double category \({\mathbb {B}}\) to the double category whose 0-cells are the double functors \({\mathbb {A}} \rightarrow {\mathbb {B}}\), whose horizontal and vertical 1-cells are the horizontal and

    更新日期:2019-12-18
  • A Combinatorial-Topological Shape Category for Polygraphs
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-11-30
    Amar Hadzihasanovic

    We introduce constructible directed complexes, a combinatorial presentation of higher categories inspired by constructible complexes in poset topology. Constructible directed complexes with a greatest element, called atoms, encompass common classes of higher-categorical cell shapes, including globes, cubes, oriented simplices, and a large sub-class of opetopes, and are closed under lax Gray products

    更新日期:2019-11-30
  • Intrinsic Schreier Split Extensions
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-11-27
    Andrea Montoli; Diana Rodelo; Tim Van der Linden

    In the context of regular unital categories we introduce an intrinsic version of the notion of a Schreier split epimorphism, originally considered for monoids. We show that such split epimorphisms satisfy the same homological properties as Schreier split epimorphisms of monoids do. This gives rise to new examples of \({\mathcal {S}}\)-protomodular categories, and allows us to better understand the

    更新日期:2019-11-27
  • Functors and Morphisms Determined by Subcategories
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-10-30
    Shijie Zhu

    We study the existence and uniqueness of minimal right determiners in various categories. Particularly in a \({{\,\mathrm{Hom}\,}}\)-finite hereditary abelian category with enough projectives, we prove that the Auslander–Reiten–Smalø–Ringel formula of the minimal right determiner still holds. As an application, we give a formula of minimal right determiners in the category of finitely presented representations

    更新日期:2019-10-30
  • Pro-compactly Finite MV-Algebras
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-10-17
    Maurice Kianpi; Jean B. Nganou

    We introduce compactly finite MV-algebras and continuous MV-algebras. We also investigate pro-compactly finite MV-algebras, which are the MV-algebras that are inverse limits of systems of compactly finite MV-algebras. We obtain that continuous MV-algebras as well as pro-compactly finite MV-algebras coincide with compact Hausdorff MV-algebras. In addition, further categorical properties of compact Hausdorff

    更新日期:2019-10-17
  • The Vietoris Monad and Weak Distributive Laws
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-10-16
    Richard Garner

    The Vietoris monad on the category of compact Hausdorff spaces is a topological analogue of the power-set monad on the category of sets. Exploiting Manes’ characterisation of the compact Hausdorff spaces as algebras for the ultrafilter monad on sets, we give precise form to the above analogy by exhibiting the Vietoris monad as induced by a weak distributive law, in the sense of Böhm, of the power-set

    更新日期:2019-10-16
  • A Unified Classification Theorem for Mal’tsev-Like Categories
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-10-15
    Nelson Martins-Ferreira

    In this paper we give unified characterizations of categories defined by variations of the Mal’tsev property.

    更新日期:2019-10-15
  • Neighbourhood Operators: Additivity, Idempotency and Convergence
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-10-11
    A. Razafindrakoto

    We define and discuss the notions of additivity and idempotency for neighbourhood and interior operators. We then propose an order-theoretic description of the notion of convergence that was introduced by D. Holgate and J. Šlapal with the help of these two properties. This will provide a rather convenient setting in which compactness and completeness can be studied via neighbourhood operators. We prove

    更新日期:2019-10-11
  • The Universal Property of Infinite Direct Sums in $$\hbox {C}^*$$C∗ -Categories and $$\hbox {W}^*$$W∗ -Categories
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-10-08
    Tobias Fritz; Bas Westerbaan

    When formulating universal properties for objects in a dagger category, one usually expects a universal property to characterize the universal object up to unique unitary isomorphism. We observe that this is automatically the case in the important special case of \(\hbox {C}^*\)-categories, provided that one uses enrichment in Banach spaces. We then formulate such a universal property for infinite

    更新日期:2019-10-08
  • On Integral Structure Types
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-09-12
    James Fullwood

    We introduce integral structure types as a categorical analogue of virtual combinatorial species. Integral structure types then categorify power series with possibly negative coefficients in the same way that combinatorial species categorify power series with non-negative rational coefficients. The notion of an operator on combinatorial species naturally extends to integral structure types, and in

    更新日期:2019-09-12
  • Algebraic Theories and Commutativity in a Sheaf Topos
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-09-09
    Boaz Haberman

    For any site of definition \(\mathcal {C}\) of a Grothendieck topos \(\mathcal {E}\), we define a notion of a \(\mathcal {C}\)-ary Lawvere theory \(\tau : \mathscr {C} \rightarrow \mathscr {T}\) whose category of models is a stack over \(\mathcal {E}\). Our definitions coincide with Lawvere’s finitary theories when \(\mathcal {C}=\aleph _0\) and \(\mathcal {E} = {{\,\mathrm{\mathbf {Set}}\,}}\). We

    更新日期:2019-09-09
  • Further Results on the Structure of (Co)Ends in Finite Tensor Categories
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-09-06
    Kenichi Shimizu

    Let \({\mathcal {C}}\) be a finite tensor category, and let \({\mathcal {M}}\) be an exact left \({\mathcal {C}}\)-module category. The action of \({\mathcal {C}}\) on \({\mathcal {M}}\) induces a functor \(\rho : {\mathcal {C}} \rightarrow \mathrm {Rex}({\mathcal {M}})\), where \(\mathrm {Rex}({\mathcal {M}})\) is the category of k-linear right exact endofunctors on \({\mathcal {M}}\). Our key observation

    更新日期:2019-09-06
  • Extensions of Filtered Ogus Structures
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-08-28
    Bruno Chiarellotto; Nicola Mazzari

    We compute the Ext group of the (filtered) Ogus category over a number field K. In particular we prove that the filtered Ogus realisation of mixed motives is not fully faithful.

    更新日期:2019-08-28
  • Maximal Lindelöf Locales
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-08-20
    Themba Dube

    For a subfit frame L, let \({\mathcal {S}}_{\mathfrak {c}}(L)\) denote the complete Boolean algebra whose elements are the sublocales of L that are joins of closed sublocales. Identifying every element of L with the open sublocale it determines allows us to view L as a subframe of \({\mathcal {S}}_{\mathfrak {c}}(L)\). With this backdrop, we say L is maximal Lindelöf if it is Lindelöf and whenever

    更新日期:2019-08-20
  • Compact Hausdorff Spaces with Relations and Gleason Spaces
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-08-13
    G. Bezhanishvili; D. Gabelaia; J. Harding; M. Jibladze

    We consider an alternate form of the equivalence between the category of compact Hausdorff spaces and continuous functions and a category formed from Gleason spaces and certain relations. This equivalence arises from the study of the projective cover of a compact Hausdorff space. This line leads us to consider the category of compact Hausdorff spaces with closed relations, and the corresponding subcategories

    更新日期:2019-08-13
  • Local Presentability of Certain Comma Categories
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-08-10
    Andrew Polonsky; Patricia Johann

    It follows from standard results that if \(\mathcal {A}\) and \(\mathcal {C}\) are locally \(\lambda \)-presentable categories and \(F : \mathcal {A}\rightarrow \mathcal {C}\) is a \(\lambda \)-accessible functor, then the comma category \(\mathsf {Id}_\mathcal {C}{\downarrow }{}F\) is locally \(\lambda \)-presentable. We show that, under the same hypotheses, \(F{\downarrow }{}\mathsf {Id}_\mathcal

    更新日期:2019-08-10
  • Crossed Modules of Monoids I: Relative Categories
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-08-10
    Gabriella Böhm

    This is the first part of a series of three strongly related papers in which three equivalent structures are studied: internal categories in categories of monoids, defined in terms of pullbacks relative to a chosen class of spans crossed modules of monoids relative to this class of spans simplicial monoids of so-called Moore length 1 relative to this class of spans. The most important examples of monoids

    更新日期:2019-08-10
  • Differential Categories Revisited
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-07-04
    R. F. Blute; J. R. B. Cockett; J.-S. P. Lemay; R. A. G. Seely

    Differential categories were introduced to provide a minimal categorical doctrine for differential linear logic. Here we revisit the formalism and, in particular, examine the two different approaches to defining differentiation which were introduced. The basic approach used a deriving transformation, while a more refined approach, in the presence of a bialgebra modality, used a codereliction. The latter

    更新日期:2019-07-04
  • Characterizations of Majority Categories
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-06-26
    Michael Hoefnagel

    In universal algebra, it is well known that varieties admitting a majority term admit several Mal’tsev-type characterizations. The main aim of this paper is to establish categorical counterparts of some of these characterizations for regular categories. We prove a categorical version of Bergman’s Double-projection Theorem: a regular category is a majority category if and only if every subobject S of

    更新日期:2019-06-26
  • Categorified Cyclic Operads
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-05-31
    Pierre-Louis Curien; Jovana Obradović

    In this paper, we introduce a notion of categorified cyclic operad for set-based cyclic operads with symmetries. Our categorification is obtained by relaxing defining axioms of cyclic operads to isomorphisms and by formulating coherence conditions for these isomorphisms. The coherence theorem that we prove has the form “all diagrams of canonical isomorphisms commute”. Our coherence results come in

    更新日期:2019-05-31
  • Distributive Laws via Admissibility
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-05-24
    Charles Walker

    This paper concerns the problem of lifting a KZ doctrine P to the 2-category of pseudo T-algebras for some pseudomonad T. Here we show that this problem is equivalent to giving a pseudo-distributive law (meaning that the lifted pseudomonad is automatically KZ), and that such distributive laws may be simply described algebraically and are essentially unique [as known to be the case in the (co)KZ over

    更新日期:2019-05-24
  • Extracting a $$\Sigma $$ Σ -Mal’tsev ( $$\Sigma $$ Σ -Protomodular) Structure from a Mal’tsev (Protomodular) Subcategory
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-05-17
    Dominique Bourn

    We give conditions on an inclusion \({\mathbb {C}}\hookrightarrow {\mathbb {D}}\) where \({\mathbb {C}}\) is a Mal’tsev (resp. protomodular) subcategory in order to produce on \({\mathbb {D}}\) a partial \(\Sigma \)-Mal’tsev (resp. \(\Sigma \)-protomodular) structure.

    更新日期:2019-05-17
  • Dynamical Systems and Sheaves
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-04-05
    Patrick Schultz; David I. Spivak; Christina Vasilakopoulou

    A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as ‘machines’ with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special cases include continuous and discrete dynamical systems (e.g. Moore machines). Additionally, morphisms between the different types of systems allow their translation

    更新日期:2019-04-05
  • Reedy Diagrams in V-Model Categories
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-04-04
    Moncef Ghazel; Fethi Kadhi

    We study the category of Reedy diagrams in a \(\mathscr {V}\)-model category. Explicitly, we show that if K is a small category, \(\mathscr {V}\) is a closed symmetric monoidal category and \(\mathscr {C}\) is a closed \(\mathscr {V}\)-module, then the diagram category \(\mathscr {V}^K\) is a closed symmetric monoidal category and the diagram category \(\mathscr {C}^K\) is a closed \(\mathscr {V}^K\)-module

    更新日期:2019-04-04
  • Classifying Subcategories in Quotients of Exact Categories
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-03-11
    Emilie Arentz-Hansen

    We classify certain subcategories in quotients of exact categories. In particular, we classify the triangulated and thick subcategories of an algebraic triangulated category, i.e. the stable category of a Frobenius category.

    更新日期:2019-03-11
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