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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, Yde Venema
core +4 more sources
What is category theory to cognitive science? Compositional representation and comparison. [PDF]
Front Psychol, 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.
Phillips S.
europepmc +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
The Information Loss of a Stochastic Map. [PDF]
Entropy (Basel), 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
Fullwood J, Parzygnat AJ.
europepmc +2 more sources
Modified Traces and the Nakayama Functor [PDF]
Algebras and Representation Theory, 2021 We organize the modified trace theory with the use of the Nakayama functor of finite abelian categories. For a linear right exact functor Σ on a finite abelian category M ${\mathscr{M}}$ , we introduce the notion of a Σ -twisted trace on the class Proj (
Taiki Shibata, K. Shimizu
semanticscholar +1 more source
The six-functor formalism for rigid analytic motives [PDF]
Forum of Mathematics, Sigma, 2020 We offer a systematic study of rigid analytic motives over general rigid analytic spaces, and we develop their six-functor formalism. A key ingredient is an extended proper base change theorem that we are able to justify by reducing to the case of ...
J. Ayoub +2 more
semanticscholar +1 more source
t-Structures with Grothendieck hearts via functor categories [PDF]
Selecta Mathematica, 2020 We study when the heart of a t -structure in a triangulated category $$\mathcal {D}$$ D with coproducts is AB5 or a Grothendieck category. If $$\mathcal {D}$$ D satisfies Brown representability, a t -structure has an AB5 heart with an injective ...
Manuel Saor'in, Jan Št’ovíček
semanticscholar +1 more source
The universal six-functor formalism [PDF]
Annals of K-theory, 2020 We prove that Morel-Voevodsky's stable $\mathbb{A}^1$-homotopy theory affords the universal six-functor formalism.
B. Drew, Martin Gallauer
semanticscholar +1 more source
Comparing the orthogonal and unitary functor calculi [PDF]
Homology, Homotopy and Applications, 2020 The orthogonal and unitary calculi give a method to study functors from the category of real or complex inner product spaces to the category of based topological spaces.
Niall Taggart
semanticscholar +1 more source
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
doaj +1 more source