样式: 排序: IF: - GO 导出 标记为已读
-
The Categorical Basis of Dynamical Entropy Appl. Categor. Struct. (IF 0.6) Pub Date : 2024-03-08 Suddhasattwa Das
-
Operads, Operadic Categories and the Blob Complex Appl. Categor. Struct. (IF 0.6) Pub Date : 2024-02-08 Michael Batanin, Martin Markl
-
Idempotent Completions of n-Exangulated Categories Appl. Categor. Struct. (IF 0.6) Pub Date : 2024-02-08 Carlo Klapproth, Dixy Msapato, Amit Shah
-
The Structure of Aisles and Co-aisles of t-Structures and Co-t-structures Appl. Categor. Struct. (IF 0.6) Pub Date : 2024-02-06 Aran Tattar
-
Algebraic Dynamical Systems in Machine Learning Appl. Categor. Struct. (IF 0.6) Pub Date : 2024-01-18
Abstract We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an iterated rewriting system defines a formal class of models into which all the main architectures for dynamic machine learning models (including recurrent neural networks, graph neural networks, and diffusion models) can be embedded. Considered in category
-
The Stone Representations for Generalized Continuous Posets Appl. Categor. Struct. (IF 0.6) Pub Date : 2024-01-16 Ao Shen, Qingguo Li
In this paper, we introduce the concepts of generalized continuous posets and present topological dualities for them. Moreover, we show that the category of generalized continuous posets and continuous morphisms is dually equivalent to the category of F-spaces and F-morphisms. In particular, some special cases are obtained, such as the topological representations for posets, domains, continuous lattices
-
Compatible Structures of Nonsymmetric Operads, Manin Products and Koszul Duality Appl. Categor. Struct. (IF 0.6) Pub Date : 2024-01-10 Huhu Zhang, Xing Gao, Li Guo
Various compatibility conditions among replicated copies of operations in a given algebraic structure have appeared in broad contexts in recent years. Taking a uniform approach, this paper presents an operadic study of compatibility conditions for nonsymmetric operads with unary and binary operations, and homogeneous quadratic and cubic relations. This generalizes the previous studies for binary quadratic
-
Generalization of the Dehornoy–Lafont Order Complex to Categories: Application to Exceptional Braid Groups Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-12-12 Owen Garnier
The homology of a Garside monoid, thus of a Garside group, can be computed efficiently through the use of the order complex defined by Dehornoy and Lafont. We construct a categorical generalization of this complex and we give some computational techniques which are useful for reducing computing time. We then use this construction to complete results of Salvetti, Callegaro and Marin regarding the homology
-
Koszul Monoids in Quasi-abelian Categories Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-12-06 Rhiannon Savage
-
Homotopy Sheaves on Generalised Spaces Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-12-04 Severin Bunk
-
Unbounded Algebraic Derivators Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-12-02 Leovigildo Alonso Tarrío, Beatriz Álvarez Díaz, Ana Jeremías López
We show that the unbounded derived category of a Grothendieck category with enough projective objects is the base category of a derivator whose category of diagrams is the full 2-category of small categories. With this structure, we give a description of the localization functor associated to a specialization closed subset of the spectrum of a commutative noetherian ring. In addition, using the derivator
-
Homotopy (Co)limits via Homotopy (Co)ends in General Combinatorial Model Categories Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-11-27 Sergey Arkhipov, Sebastian Ørsted
We prove and explain several classical formulae for homotopy (co)limits in general (combinatorial) model categories which are not necessarily simplicially enriched. Importantly, we prove versions of the Bousfield–Kan formula and the fat totalization formula in this complete generality. We finish with a proof that homotopy-final functors preserve homotopy limits, again in complete generality.
-
Partialising Institutions Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-11-15 Răzvan Diaconescu
\({3/2}\)-Institutions have been introduced as an extension of institution theory that accommodates implicitly partiality of the signature morphisms together with its syntactic and semantic effects. In this paper we show that ordinary institutions that are equipped with an inclusion system for their categories of signatures generate naturally \({3/2}\)-institutions with explicit partiality for their
-
Compact Hausdorff Locales in Presheaf Toposes Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-10-19 Simon Henry, Christopher Townsend
We prove that for any small category \({\mathcal {C}}\), the category \(\textbf{KHausLoc}_{\hat{{\mathcal {C}}}}\) of compact Hausdorff locales in the presheaf topos \(\hat{{\mathcal {C}}}\), is equivalent to the category of functors \({\mathcal {C}} \rightarrow \textbf{KHausLoc}\).
-
Continuous Nakayama Representations Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-10-03 Job Daisie Rock, Shijie Zhu
-
Pervin Spaces and Frith Frames: Bitopological Aspects and Completion Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-09-30 Célia Borlido, Anna Laura Suarez
A Pervin space is a set equipped with a bounded sublattice of its powerset, while its pointfree version, called Frith frame, consists of a frame equipped with a generating bounded sublattice. It is known that the dual adjunction between topological spaces and frames extends to a dual adjunction between Pervin spaces and Frith frames, and that the latter may be seen as representatives of certain quasi-uniform
-
From Gs-monoidal to Oplax Cartesian Categories: Constructions and Functorial Completeness Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-09-28 Tobias Fritz, Fabio Gadducci, Davide Trotta, Andrea Corradini
-
Nonexistence of Colimits in Naive Discrete Homotopy Theory Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-09-27 Daniel Carranza, Krzysztof Kapulkin, Jinho Kim
We show that the quasicategory defined as the localization of the category of (simple) graphs at the class of A-homotopy equivalences does not admit colimits. In particular, we settle in the negative the question of whether the A-homotopy equivalences in the category of graphs are part of a model structure.
-
Diagrammatic Presentations of Enriched Monads and Varieties for a Subcategory of Arities Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-09-22 Rory B. B. Lucyshyn-Wright, Jason Parker
The theory of presentations of enriched monads was developed by Kelly, Power, and Lack, following classic work of Lawvere, and has been generalized to apply to subcategories of arities in recent work of Bourke–Garner and the authors. We argue that, while theoretically elegant and structurally fundamental, such presentations of enriched monads can be inconvenient to construct directly in practice, as
-
On the Structure of an Internal Groupoid Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-09-18 Nelson Martins-Ferreira
The category of internal groupoids (in an arbitrary category) is shown to be equivalent to the full subcategory of so called involutive-2-links that are unital and associative.
-
Coactions on $$C^*$$ -Algebras and Universal Properties Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-09-07 Erik Bédos, S. Kaliszewski, John Quigg, Jonathan Turk
It is well-known that the maximalization of a coaction of a locally compact group on a C*-algebra enjoys a universal property. We show how this important property can be deduced from a categorical framework by exploiting certain properties of the maximalization functor for coactions. We also provide a dual proof for the universal property of normalization of coactions.
-
A Halmos–von Neumann Theorem for Actions of General Groups Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-09-08 Patrick Hermle, Henrik Kreidler
We give a new categorical approach to the Halmos–von Neumann theorem for actions of general topological groups. As a first step, we establish that the categories of topological and measure-preserving irreducible systems with discrete spectrum are equivalent. This allows to prove the Halmos–von Neumann theorem in the framework of topological dynamics. We then use the Pontryagin and Tannaka–Krein duality
-
Admissibility of Localizations of Crossed Modules Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-09-08 Olivia Monjon, Jérôme Scherer, Florence Sterck
-
Deriving Dualities in Pointfree Topology from Priestley Duality Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-09-01 G. Bezhanishvili, S. Melzer
-
Extension of Topological Groupoids and Hurewicz Morphisms Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-08-28 Saikat Chatterjee, Praphulla Koushik
In this paper, we introduce the notion of a topological groupoid extension and relate it to the already existing notion of a gerbe over a topological stack. We further study the properties of a gerbe over a Hurewicz (resp. Serre) stack.
-
Hopf Monads: A Survey with New Examples and Applications Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-08-27 Aryan Ghobadi
We survey the theory of Hopf monads on monoidal categories, and present new examples and applications. As applications, we utilise this machinery to present a new theory of cross products, as well as analogues of the Fundamental Theorem of Hopf algebras and Radford’s biproduct Theorem for Hopf algebroids. Additionally, we describe new examples of Hopf monads which arise from Galois and Ore extensions
-
Maximal Ordered Groupoids and a Galois Correspondence for Inverse Semigroup Orthogonal Actions Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-08-21 Wesley G. Lautenschlaeger, Thaísa Tamusiunas
We introduce maximal ordered groupoids and study some of their properties. Also, we use the Ehresmann–Schein–Nambooripad Theorem, which establishes a one-to-one correspondence between inverse semigroups and a class of ordered groupoids, to prove a Galois correspondence for the case of inverse semigroups acting orthogonally on commutative rings.
-
Categorical View of the Partite Lemma in Structural Ramsey Theory Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-08-04 Sebastian Junge
We construct the main object of the Partite Lemma as the colimit over a certain diagram. This gives a purely category theoretic take on the Partite Lemma and establishes the canonicity of the object. Additionally, the categorical point of view allows us to unify the direct Partite Lemma in Nešetřil and Rödl (J Comb Theory Ser A 22(3):289–312, 1977; J Comb Theory Ser A 34(2):183–201, 1983; Discrete
-
Weighted Colimits of 2-Representations and Star Algebras Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-07-22 Mateusz Stroiński
-
-
Yoneda Lemma for Simplicial Spaces Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-07-11 Nima Rasekh
-
R-Linear Triangulated Categories and Stability Conditions Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-06-29 Kotaro Kawatani, Hiroyuki Minamoto
Let R be a commutative ring. We introduce the notion of support of a object in an R-linear triangulated category. As an application, we study the non-existence of Bridgeland stability condition on R-linear triangulated categories.
-
De Vries Powers and Proximity Specker Algebras Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-04-21 G. Bezhanishvili, L. Carai, P. J. Morandi, B. Olberding
-
Additive Grothendieck Pretopologies and Presentations of Tensor Categories Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-04-20 Kevin Coulembier
We study how tensor categories can be presented in terms of rigid monoidal categories and Grothendieck topologies and show that such presentations lead to strong universal properties. As the main tool in this study, we define a notion on preadditive categories which plays a role similar to (a generalisation of) the notion of a Grothendieck pretopology on an unenriched category. Each such additive pretopology
-
Profunctors Between Posets and Alexander Duality Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-04-10 Gunnar Fløystad
-
Free gs-Monoidal Categories and Free Markov Categories Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-04-08 Tobias Fritz, Wendong Liang
-
Inner Automorphisms of Presheaves of Groups Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-04-08 Jason Parker
It has been proven by Schupp and Bergman that the inner automorphisms of groups can be characterized purely categorically as those group automorphisms that can be coherently extended along any outgoing homomorphism. One is thus motivated to define a notion of (categorical) inner automorphism in an arbitrary category, as an automorphism that can be coherently extended along any outgoing morphism, and
-
Distributive Laws for Relative Monads Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-04-05 Gabriele Lobbia
We introduce the notion of a distributive law between a relative monad and a monad. We call this a relative distributive law and define it in any 2-category \(\mathcal {K}\). In order to do that, we introduce the 2-category of relative monads in a 2-category \(\mathcal {K}\) with relative monad morphisms and relative monad transformations as 1- and 2-cells, respectively. We relate our definition to
-
Rings and Modules in Kan Spectra Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-04-04 R. Chen, I. Kriz, A. Pultr
The purpose of this paper is to set up derived categories of sheaves of \(E_\infty \)-rings and modules over non-derived sites, in particular over topological spaces. This theory opens up certain new capabilities in spectral algebra. For example, as outlined in the last section of the present paper, using these concepts, one can conjecture a spectral algebra-based generalization of the geometric Langlands
-
Clifford’s Theorem for Orbit Categories Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-04-03 Alexander Zimmermann
Clifford theory relates the representation theory of finite groups to those of a fixed normal subgroup by means of induction and restriction, which is an adjoint pair of functors. We generalize this result to the situation of a Krull-Schmidt category on which a finite group acts as automorphisms. This then provides the orbit category introduced by Cibils and Marcos, and studied intensively by Keller
-
Locally Type $$\text {FP}_{{\varvec{n}}}$$ and $${\varvec{n}}$$ -Coherent Categories Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-03-27 Daniel Bravo, James Gillespie, Marco A. Pérez
We study finiteness conditions in Grothendieck categories by introducing the concepts of objects of type \(\textrm{FP}_n\) and studying their closure properties with respect to short exact sequences. This allows us to propose a notion of locally type \(\textrm{FP}_n\) categories as a generalization of locally finitely generated and locally finitely presented categories. We also define and study the
-
Higher Auslander’s defect and classifying substructures of $$\varvec{n}$$ -exangulated categories Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-03-20 Jiangsheng Hu, Yajun Ma, Dongdong Zhang, Panyue Zhou
Herschend–Liu–Nakaoka introduced the notion of an n-exangulated category. It is not only a higher dimensional analogue of extriangulated categories defined by Nakaoka–Palu, but also gives a simultaneous generalization of n-exact categories and \((n+2)\)-angulated categories. In this article, we give an n-exangulated version of Auslander’s defect and Auslander–Reiten duality formula. Moreover, we also
-
Closed and Open Maps for Partial Frames Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-03-15 John Frith, Anneliese Schauerte
-
Commutative Objects, Central Morphisms and Subtractors in Subtractive Categories Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-03-12 Vaino Tuhafeni Shaumbwa
-
Some Modifications of Hull Operators in Archimedean Lattice-Ordered Groups with Weak Unit Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-02-28 Ricardo E. Carrera, Anthony W. Hager
\({\textbf {W}}\) denotes the category, or class of algebras, in the title. A hull operator (ho) in \({\textbf {W}}\) is a function \(\textbf{ho} {\textbf {W}}\overset{h}{\longrightarrow }\ {\textbf {W}}\) which can be called an essential closure operator. The family of these, denoted \(\textbf{ho} {\textbf {W}}\), is a proper class and a complete lattice in the ordering as functions “pointwise", with
-
Descent for internal multicategory functors Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-01-17 Rui Prezado, Fernando Lucatelli Nunes
-
Trace Decategorification of Categorified Quantum sl(3) Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-01-11 Marko Živković
We prove that the trace of categorified quantum \(\mathfrak {sl}_3\) introduced by Khovanov and Lauda can also be identified with quantum \(\mathfrak {sl}_3\), thus providing an alternative way of decategorification. This is the second step of trace decategorification of quantum \(\mathfrak {sl}_n\) groups over the integers, the first being the \(\mathfrak {sl}_2\) case. The main technique used is
-
A symmetric approach to higher coverings in categorical Galois theory Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-01-11 Fara Renaud, Tim Van der Linden
-
Local Cohen–Macaulay DG-Modules Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-01-03 Xiaoyan Yang, Yanjie Li
Let A be a commutative noetherian local DG-ring with bounded cohomology. For local Cohen–Macaulay DG-modules with constant amplitude, we obtain an explicit formula for the sequential depth, show that Cohen–Macaulayness is stable under localization and give several equivalent definitions of maximal local Cohen–Macaulay DG-modules over local Cohen–Macaulay DG-rings. We also provide some characterizations
-
Minimal Models of Some Differential Graded Modules Appl. Categor. Struct. (IF 0.6) Pub Date : 2023-01-03 Berrin Şentürk, Özgün Ünlü
Minimal models of chain complexes associated with free torus actions on spaces have been extensively studied in the literature. In this paper, we discuss these constructions using the language of operads. The main goal of this paper is to define a new Koszul operad that has projections onto several of the operads used in these minimal model constructions.
-
Ramsey Properties of Products and Pullbacks of Categories and the Grothendieck Construction Appl. Categor. Struct. (IF 0.6) Pub Date : 2022-12-29 Dragan Mašulović
-
Unitless Frobenius Quantales Appl. Categor. Struct. (IF 0.6) Pub Date : 2022-12-27 Cédric de Lacroix, Luigi Santocanale
-
q-Tensor and Exterior Centers, Related Degrees and Capability Appl. Categor. Struct. (IF 0.6) Pub Date : 2022-12-26 Raimundo Bastos, Ricardo de Oliveira, Guram Donadze, Noraí Romeu Rocco
We introduce intermediate commutators and study their degrees. We define \((q, \{\})\)-capable groups and prove that a group G is \((q, \{\})\)-capable if and only if \(Z^{\wedge }_{(q, \{\})}(G)=1\).
-
A Simplicial Category for Higher Correspondences Appl. Categor. Struct. (IF 0.6) Pub Date : 2022-12-27 Redi Haderi
-
A Pullback Diagram in the Coarse Category Appl. Categor. Struct. (IF 0.6) Pub Date : 2022-12-27 Elisa Hartmann
This paper studies the asymptotic product of two metric spaces. It is well defined if one of the spaces is visual or if both spaces are geodesic. In this case the asymptotic product is the pullback of a limit diagram in the coarse category. Using this product construction we can define a homotopy theory on coarse metric spaces in a natural way. We prove that all finite colimits exist in the coarse
-
Operators Between Classes of Modules Given by Preradicals Appl. Categor. Struct. (IF 0.6) Pub Date : 2022-12-19 Alejandro Alvarado García, César Cejudo Castilla, Mauricio Medina Bárcenas, Ivan Fernando Vilchis Montalvo
Given a preradical we obtain operators between classes modules with closure properties. These operators turn out to be prenuclei and under suitable conditions nuclei. In particular, for the lattices of natural and conatural classes we obtain some nice properties and characterize some classes of rings.
-
-
Semantic Factorization and Descent Appl. Categor. Struct. (IF 0.6) Pub Date : 2022-11-15 Fernando Lucatelli Nunes
-
2-Cartesian Fibrations I: A Model for $$\infty $$ -Bicategories Fibred in $$\infty $$ -Bicategories Appl. Categor. Struct. (IF 0.6) Pub Date : 2022-09-28 Fernando Abellán García, Walker H. Stern
-
Matrix Taxonomy and Bourn Localization Appl. Categor. Struct. (IF 0.6) Pub Date : 2022-09-21 Michael Hoefnagel, Pierre-Alain Jacqmin