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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.
Jacques Carette, Jason Hu
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Category Theory in Coq 8.5 [PDF]
International Conference on Formal Structures for Computation and Deduction, 2015 We report on our experience implementing category theory in Coq 8.5. The repository of this development can be found at https://bitbucket.org/amintimany/categories/.
Jacobs, Bart, Timany, Amin
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Could ∞-Category Theory Be Taught to Undergraduates? [PDF]
Notices of the American Mathematical Society, 2023 The extension of ordinary category theory to $\infty$-categories at the start of the 21st century was a spectacular achievement pioneered by Joyal and Lurie with contributions from many others. Unfortunately, the technical arguments required to solve the
E. Riehl
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An Enriched Category Theory of Language: From Syntax to Semantics [PDF]
La Matematica, 2021 State of the art language models return a natural language text continuation from any piece of input text. This ability to generate coherent text extensions implies significant sophistication, including a knowledge of grammar and semantics. In this paper,
T. Bradley +2 more
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MultiCategory: Multi-model Query Processing Meets Category Theory and Functional Programming [PDF]
Proceedings of the VLDB Endowment, 2021 The variety of data is one of the important issues in the era of Big Data. The data are naturally organized in different formats and models, including structured data, semi-structured data, and unstructured data. Prior research has envisioned an approach
Valter Uotila +5 more
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A Formal Logic for Formal Category Theory
Foundations of Software Science and Computation Structure, 2023 . We present a domain-specific type theory for constructions and proofs in category theory. The type theory axiomatizes notions of category, functor, profunctor and a generalized form of natural transformations.
Max S. New, Daniel R. Licata
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On continuous 2-category symmetries and Yang-Mills theory [PDF]
Journal of High Energy Physics, 2022 We study a 4d gauge theory U(1)N−1 ⋊ SN obtained from a U(1)N−1 theory by gauging a 0-form symmetry SN. We show that this theory has a global continuous 2-category symmetry, whose structure is particularly rich for N > 2. This example allows us to draw a
Andrea Antinucci +2 more
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Acta Crystallographica Section A: Foundations and Advances, 2021 An invitation to applied category theory seven sketches. p d f an invitation to applied category theory seven. sevensketchesinpositionality. an invitation to applied category theory seven sketches. an invitation to applied category theory seven sketches.
B. Stöger
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A unified representation and transformation of multi-model data using category theory
Journal of Big Data, 2022 The support for multi-model data has become a standard for most of the existing DBMSs. However, the step from a conceptual (e.g., ER or UML) schema to a logical multi-model schema of a particular DBMS is not straightforward.
Pavel Koupil, I. Holubová
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Pretorsion theories in general categories [PDF]
Journal of Pure and Applied Algebra, 2021 22 ...
Alberto Facchini +2 more
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