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  • 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
  • Cofibrantly Generated Lax Orthogonal Factorisation Systems
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-02-27
    Ignacio López Franco

    The present note has three aims. First, to complement the theory of cofibrant generation of algebraic weak factorisation systems (awfss) to cover some important examples that are not locally presentable categories. Secondly, to prove that cofibrantly kz-generated awfss (a notion we define) are always lax orthogonal. Thirdly, to show that the two known methods of building lax orthogonal awfss, namely

    更新日期:2019-02-27
  • Homotopical Algebra for Lie Algebroids
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-02-18
    Joost Nuiten

    We construct Quillen equivalent semi-model structures on the categories of dg-Lie algebroids and \(L_\infty \)-algebroids over a commutative dg-algebra in characteristic zero. This allows one to apply the usual methods of homotopical algebra to dg-Lie algebroids: for example, every Lie algebroid can be resolved by dg-Lie algebroids that arise from dg-Lie algebras, i.e. whose anchor map is zero. As

    更新日期:2019-02-18
  • The Spectrum of the Singularity Category of a Category Algebra
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-02-13
    Ren Wang

    Let \({\mathscr {C}}\) be a finite projective EI category and k be a field. The singularity category of the category algebra \(k{\mathscr {C}}\) is a tensor triangulated category. We compute its spectrum in the sense of Balmer.

    更新日期:2019-02-13
  • Homotopical Adjoint Lifting Theorem
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-02-12
    David White; Donald Yau

    This paper provides a homotopical version of the adjoint lifting theorem in category theory, allowing for Quillen equivalences to be lifted from monoidal model categories to categories of algebras over colored operads. The generality of our approach allows us to simultaneously answer questions of rectification and of changing the base model category to a Quillen equivalent one. We work in the setting

    更新日期:2019-02-12
  • On a Model Invariance Problem in Homotopy Type Theory
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-02-01
    Anthony Bordg

    In this article, the author endows the functor category \([\mathbf {B}(\mathbb {Z}_2),\mathbf {Gpd}]\) with the structure of a type-theoretic fibration category with a univalent universe, using the so-called injective model structure. This gives a new model of Martin-Löf type theory with dependent sums, dependent products, identity types and a univalent universe. This model, together with the model

    更新日期:2019-02-01
  • On the Degree in Categories of Complexes of Fixed Size
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-02-01
    Claudia Chaio; Isabel Pratti; María José Souto Salorio

    We consider \(\Lambda \) an artin algebra and \(n \ge 2\). We study how to compute the left and right degrees of irreducible morphisms between complexes in a generalized standard Auslander–Reiten component of \({{\mathbf {C_n}}(\mathrm{proj}\, \Lambda )}\) with length. We give conditions under which the kernel and the cokernel of irreducible morphisms between complexes in \({\mathbf {C_n}}(\mathrm{proj}\

    更新日期:2019-02-01
  • Concerning P -Sublocales and Disconnectivity
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-01-23
    Themba Dube

    Motivated by certain types of ideals in pointfree functions rings, we define what we call P-sublocales in completely regular frames. They are the closed sublocales that are interior to the zero-sublocales containing them. We call an element of a frame L that induces a P-sublocale a P-element, and denote by \({{\,\mathrm{Pel}\,}}(L)\) the set of all such elements. We show that if L is basically disconnected

    更新日期:2019-01-23
  • Hom–Tensor Categories and the Hom–Yang–Baxter Equation
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-01-16
    Florin Panaite; Paul T. Schrader; Mihai D. Staic

    We introduce a new type of categorical object called a hom–tensor category and show that it provides the appropriate setting for modules over an arbitrary hom-bialgebra. Next we introduce the notion of hom-braided category and show that this is the right setting for modules over quasitriangular hom-bialgebras. We also show how the Hom–Yang–Baxter equation fits into this framework and how the category

    更新日期:2019-01-16
  • Quotients of d-Frames
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-01-05
    Tomáš Jakl; Achim Jung; Aleš Pultr

    It is shown that every d-frame admits a complete lattice of quotients. Quotienting may be triggered by a binary relation on one of the two constituent frames, or by changes to the consistency or totality structure, but as these are linked by the reasonableness conditions of d-frames, the result in general will be that both frames are factored and both consistency and totality are increased.

    更新日期:2019-01-05
  • Presheaves Over a Join Restriction Category
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-01-04
    Daniel Lin

    Just as the presheaf category is the free cocompletion of any small category, there is an analogous notion of free cocompletion for any small restriction category. In this paper, we extend the work on restriction presheaves to presheaves over join restriction categories, and show that the join restriction category of join restriction presheaves is equivalent to some partial map category of sheaves

    更新日期:2019-01-04
  • Co-Gorenstein Algebras
    Appl. Categor. Struct. (IF 0.552) Pub Date : 2019-01-04
    Sondre Kvamme; René Marczinzik

    We review the theory of Co-Gorenstein algebras, which was introduced in Beligiannis (Commun Algebra 28(10):4547–4596, 2000). We show a connection between Co-Gorenstein algebras and the Nakayama and Generalized Nakayama conjecture.

    更新日期:2019-01-04
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