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What is category theory to cognitive science? Compositional representation and comparison [PDF]

Frontiers in Psychology, 2022
Category theorists and cognitive scientists study the structural (analogical) relations between domains of interest albeit in different contexts, that is, formal and psychological systems, respectively.
Steven Phillips
doaj   +2 more sources

Tambarization of a Mackey functor and its application to the Witt-Burnside construction [PDF]

arXiv, 2010
For an arbitrary group $G$, a (semi-)Mackey functor is a pair of covariant and contravariant functors from the category of $G$-sets, and is regarded as a $G$-bivariant analog of a commutative (semi-)group. In this view, a $G$-bivariant analog of a (semi-)ring should be a (semi-)Tambara functor.
Nakaoka, Hiroyuki
arxiv   +4 more sources

Derived category of weak chain U-complexes [PDF]

Heliyon
In this paper, we define the derived category of weak chain U-complexes, and we give a characterization of any weak chain U-complex as an object in the right bounded homotopy category of weak chain U-complexes of projective modules.
Fajar Yuliawan, Intan Muchtadi-Alamsyah, Valerian Pratama, Gustina Elfiyanti   +3 more
doaj   +2 more sources

Biset functors for categories [PDF]

arXiv, 2023
We introduce the theory of biset functors defined on finite categories. Previously, biset functors have been defined on groups, and in that context they are closely related to Mackey functors. Standard examples on groups include representation rings, the Burnside ring and group cohomology.
arxiv   +3 more sources

Morita theorems for functor categories [PDF]

Transactions of the American Mathematical Society, 1972
We generalize the Morita theorems to certain functor categories using properties of adjoint functors.
David C. Newell
openalex   +3 more sources

The functor category Fquad [PDF]

, 2006
In this paper, we define the functor category Fquad associated to vector spaces over the field with two elements, F\_2, equipped with a quadratic form. We show the existence of a fully-faithful, exact functor : \F \to Fquad, which preserves simple objects, where \F is the category of functors from the category of finite dimensional F\_2-vector spaces
Christine Vespa
openalex   +4 more sources

Quadratic functors on pointed categories [PDF]

Advances in Mathematics, 2010
64 ...
Manfred Hartl, Christine Vespa
  +7 more sources

Categories and Functors [PDF]

Pure and Applied Mathematics, 1970
In Chapter I we discussed various algebraic structures (rings, abelian groups, modules) and their appropriate transformations (homomorphisms). We also saw how certain constructions (for example, the formation of HomΛ(A, B) for given Λ-modules A, B) produced new structures out of given structures.
Peter Hilton, Peter Hilton, Urs Stammbach   +2 more
openaire   +4 more sources

On $\ast$-measure monads on the category of ultrametric spaces

Karpatsʹkì Matematičnì Publìkacìï, 2022
The functor of $\ast$-measures of compact support on the category of ultrametric spaces and non-expanding maps is introduced in the previous publication of the authors.
Kh.O. Sukhorukova, M.M. Zarichnyi
doaj   +1 more source

Strongly Complete Logics for Coalgebras [PDF]

Logical Methods in Computer Science, 2012
Coalgebras for a functor model different types of transition systems in a uniform way. This paper focuses on a uniform account of finitary logics for set-based coalgebras.
Alexander Kurz, Jiri Rosicky
doaj   +1 more source