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Category theory for operational semantics
Theoretical Computer Science, 2004 AbstractWe use the concept of a distributive law of a monad over a copointed endofunctor to define and develop a reformulation and mild generalisation of Turi and Plotkin's notion of an abstract operational rule. We make our abstract definition and give a precise analysis of the relationship between it and Turi and Plotkin's definition.
Marina Lenisa +2 more
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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
semanticscholar +1 more source
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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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
doaj +1 more source
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
semanticscholar +1 more source
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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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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