50 papers
This paper establishes the (co)completeness of the category of small categories () by explicitly constructing specific weighted colimits that are equivalent to the existence of the homotopy category functor, thereby providing a systematic elementary approach to justify these limits and reformulate constructions like coequalizers and localizations.
This paper presents the proceedings of the Eighth International Conference on Applied Category Theory (ACT2025), held at the University of Florida in June 2025, which featured a diverse collection of contributions spanning pure and applied disciplines such as computer science, quantum computation, and chemistry.
This paper develops a higher-order abstract GSOS framework that represents operational semantics via pointed higher-order GSOS laws, thereby establishing general compositionality results for higher-order languages like the SKI and -calculi.
This paper establishes a folklore theorem characterizing the embeddability of partial groups in groups via unique parenthesization of words, investigates examples of non-embeddable cases, and proves that a partial groupoid embeds in a groupoid if and only if its reduction embeds in a group.
This paper generalizes signed directed graphs to monoid-labeled graphs to model complex systems, introducing three types of morphisms and constructing corresponding symmetric monoidal double categories of open graphs to analyze feedback loops via homology with coefficients in a commutative monoid and a Mayer-Vietoris exact sequence.
This paper establishes a comprehensive -operadic framework for embedding calculus by analyzing towers of truncated right-modules over unital -operads to generalize Goodwillie-Weiss theory to bordism categories, derive new variants for topological and configuration embeddings, and prove key results on convergence, delooping, and homology 4-spheres.
This paper investigates -categories by comparing the -categories obtained via core and localization functors in the limit , demonstrating that the latter is a reflective localization of the former while also exploring intermediate localizations arising from coinductive notions of invertibility.
These lecture notes provide a brief introduction to category theory concepts, specifically initial algebras and monads, tailored to their applications in defining datatypes, recursive functions, and effects within functional programming.
This paper establishes that a broad class of non-abelian monoidal categories can be realized as subcategories of tilting objects within abelian highest weight categories by utilizing a monoidal enhancement of semi-infinite Ringel duality, a framework that further yields monoidal structures on representations of affine Lie algebras at positive levels.
This paper characterizes split extensions with strong section in the variety of hoops and its key subvarieties using strong external actions, establishing a connection to W. Rump's semidirect product construction in L-algebras and illustrating the theory through the double negation example in BL-algebras.
This paper establishes a bridge between homotopy type theory and information theory by defining probability types, demonstrating that homotopy cardinality respects dependent sums but not products, and deriving Shannon entropy and its chain rule as the homotopy cardinality of specific types constructed via deloopings of finite cyclic groups.
This paper investigates a five-sequence of adjoint functors induced by functions between vertex sets of simplicial complexes, utilizing this structure to establish three categorical frameworks where the Stanley-Reisner correspondence yields dualities with commutative monomial rings.
This paper proves a conjecture by Brochier, Jordan, Safronov, and Snyder that characterizes fully-dualizable and invertible -algebras within higher Morita categories, thereby identifying the specific algebraic structures that generate -dimensional and invertible topological quantum field theories.
This paper introduces one-sided --Gorenstein categories as a generalization of Gorenstein categories, establishes equivalent characterizations based on relative projective and injective dimensions, and derives a necessary condition for the validity of the Wakamatsu tilting conjecture.
This paper presents complete diagrammatic axiomatisations for Kullback-Leibler and Rényi divergences by characterizing them as quantitative enrichments of stochastic matrix categories under both Kronecker product and direct sum monoidal structures within a graphical string diagram framework.
This paper establishes a stability theorem for minimal projective resolutions of modules over finite metric posets by proving that a newly defined bottleneck distance between resolutions is bounded above by the Galois transport distance, thereby generalizing classical bottleneck stability to multiparameter persistence and providing a stability framework for Möbius homology.
This paper establishes the previously unprinted universal property of the bicategory of modules () constructed from -enriched categories, presenting it as an objective generalization of Joyal's homological functors that characterizes the inclusion of a bicategory into its module bicategory as a completion with respect to freely adjoining lax colimits.
The paper demonstrates that various categories of trees, including the dendroidal category , the category of trees with a -action, and the category of genuine equivariant trees , can be modeled as Grothendieck constructions on categories of trees with a fixed set of leaves.
This paper investigates non-semisimple near-group categories in the braided setting, proving that non-degenerate instances are braided simple extensions of with specific Lagrangian properties, while general cases arise canonically as extensions by the Picard group of a symmetric subcategory.
This paper provides a complete characterization of all model category structures on finite lattices by utilizing transfer systems, thereby establishing new connections between abstract homotopy theory and equivariant methods.