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Applied Categorical Structures

A Journal Devoted to Applications of Categorical Methods in Algebra, Analysis, Order, Topology and Computer Science

Applied Categorical Structures OnlineFirst articles

13-10-2020 Open Access

A Constructive Approach to Freyd Categories

We discuss Peter Freyd’s universal way of equipping an additive category $$\mathbf {P}$$ P with cokernels from a constructive point of view. The so-called Freyd category $$\mathcal {A}(\mathbf {P})$$ A ( P ) is abelian if and only if $$\mathbf …

10-10-2020

Gabriel–Zisman Cohomology and Spectral Sequences

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 …

28-09-2020

The Kechris–Pestov–Todorčević Correspondence from the Point of View of Category Theory

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 …

24-09-2020 Open Access

Exponential Functions in Cartesian Differential Categories

In this paper, we introduce differential exponential maps in Cartesian differential categories, which generalizes the exponential function $$e^x$$ e x from classical differential calculus. A differential exponential map is an endomorphism which is …

02-09-2020

Different Exact Structures on the Monomorphism Categories

Let $${\mathcal {X}}$$ X be a contravariantly finite resolving subcategory of $${\mathrm{{mod\text{- }}}}\varLambda $$ mod - Λ , the category of finitely generated right $$\varLambda $$ Λ -modules. We associate to $${\mathcal {X}}$$ X the …

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About this journal

Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant.

Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.

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