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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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Category Theory In Geography? [PDF]
Quaestiones Geographicae, 2015 Is mathematical category theory a unifying tool for geography? Here we look at a few basic category theoretical ideas and interpret them in geographic example. We also offer links to indicate how category theory has been used as such in other disciplines.
Arlinghaus Sandra L., Kerski Joseph
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A category theory perspective on the Language of Thought: LoT is universal [PDF]
Frontiers in PsychologyThe Language of Thought (LoT) hypothesis proposes that some collections of mental states and processes are symbol systems to explain language-like systematic properties of thought.
Steven Phillips
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Category theory of symbolic dynamics
Theoretical Computer Science, 2015 We study the central objects of symbolic dynamics, that is, subshifts and block maps, from the perspective of basic category theory, and present several natural categories with subshifts as objects and block maps as morphisms. Our main goals are to find universal objects in these symbolic categories, to classify their block maps based on their category
Ilkka Torma, Ville Salo
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Compounds, 2023 “Mathematical chemistry” as an academic field is said to have been proposed by Weyl in the 20th century as a way of thinking that abstracts and expresses “variables”, “symbols” and “functions” [...]
Takashiro Akitsu
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Category theory and organic electronics
Physics Open, 2023 Inorganic semiconductors and conducting polymers are described by band conduction models with delocalized electrons, whereas small-molecule organic compounds are described by hopping conduction between localized molecular orbitals.
Jun-ichi Takahashi
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Category Theory for Programming
CoRR, 2022 In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical characterization of datatypes and recursive functions on them. Secondly, we study monads, which give a mathematical framework
Benedikt Ahrens, Kobe Wullaert
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Formalizing category theory in Agda [PDF]
Proceedings of the 10th ACM SIGPLAN International Conference on Certified Programs and Proofs, 2021 The generality and pervasiness of category theory in modern mathematics makes it a frequent and useful target of formalization. It is however quite challenging to formalize, for a variety of reasons. Agda currently (i.e. in 2020) does not have a standard, working formalization of category theory. We document our work on solving this dilemma.
Jason Z. S. Hu, Jacques Carette
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Soft category theory -an introduction [PDF]
Journal of Hyperstructures, 2013 The soft category theory offers a way to study soft theories developed so far more generally. The main purpose of this paper is to introduce the basic notions of the theory of soft categories, to present some introductory results of the theory.
S. K. Sardar, Sugato Gupta
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Lax orthogonal factorisations in monad-quantale-enriched categories [PDF]
Logical Methods in Computer Science, 2017 We show that, for a quantale $V$ and a $\mathsf{Set}$-monad $\mathbb{T}$ laxly extended to $V$-$\mathsf{Rel}$, the presheaf monad on the category of $(\mathbb{T},V)$-categories is simple, giving rise to a lax orthogonal factorisation system (lofs) whose ...
Maria Manuel Clementino +1 more
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