Results 1 to 10 of about 13,741 (235)
Transactions of the American Mathematical Society, 1958 "Adjoint functors assist in reincorporating the subjective into its rightful place as a part of the objective so that it can organically reflect the objective" (Lawvere and Rosebrugh (2003), Sets for Mathematics, Cambridge University Press, p. 239).
Daniel M. Kan
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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
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The Information Loss of a Stochastic Map [PDF]
Entropy, 2021 We provide a stochastic extension of the Baez–Fritz–Leinster characterization of the Shannon information loss associated with a measure-preserving function. This recovers the conditional entropy and a closely related information-theoretic measure that we
James Fullwood, Arthur J. Parzygnat
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Dirichlet Functors are Contravariant Polynomial Functors [PDF]
arXiv, 2020 Polynomial functors are sums of covariant representable functors from the category of sets to itself. They have a robust theory with many applications -- from operads and opetopes to combinatorial species. In this paper, we define a contravariant analogue of polynomial functors: Dirichlet functors. We develop the basic theory of Dirichlet functors, and
Myers, David Jaz, Spivak, David I.
arxiv +3 more sources
Derivation functors and Lusztig's induction functors [PDF]
arXiv, 2022 Lusztig proved the compatibility of induction functors and restriction functors for Lusztig's perverse sheaves. Fang-Lan-Xiao established a categorification of Green's formula and gave a sheaf-level proof of this compatibility for all semisimple complexes.
arxiv +3 more sources
The tensor product of functors; satellites; and derived functors
Journal of Algebra, 1968 Janet L Fisher
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Predicting Change in Emotion through Ordinal Patterns and Simple Symbolic Expressions
Mathematics, 2022 Human interlocutors may use emotions as an important signaling device for coordinating an interaction. In this context, predicting a significant change in a speaker’s emotion may be important for regulating the interaction.
Yair Neuman, Yochai Cohen
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Geometrical properties of the space of idempotent probability measures
Applied General Topology, 2021 Although traditional and idempotent mathematics are "parallel'', by an application of the category theory we show that objects obtained the similar rules over traditional and idempotent mathematics must not be "parallel''.
Kholsaid Fayzullayevich Kholturayev
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Applied Categorical Structures, 2016 Complete version, added more material, small corrections; 40 pages, 1 ...
Masulovic, Dragan, Wieslaw, Kubis
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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
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