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Category theory for operational semantics
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]
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]
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]
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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“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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On continuous 2-category symmetries and Yang-Mills theory [PDF]
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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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
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]
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Alberto Facchini+2 more
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It is well known that Zermelo-Fraenkel Set Theory (ZF), despite its usefulness as a foundational theory for mathematics, has two unwanted features: it cannot be written down explicitly due to its infinitely many axioms, and it has a countable model due ...
Marcoen J. T. F. Cabbolet
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