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DOI: 10.4230/LIPIcs.CALCO.2021.1

Distributive Laws for Lawvere Theories (Invited Talk)

Authors: Eugenia Cheng

Published in: LIPIcs, Volume 211, 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)

Abstract

Distributive laws give a way of combining two algebraic structures expressed as monads; in this work we propose a theory of distributive laws for combining algebraic structures expressed as Lawvere theories. We propose four approaches, involving profunctors, monoidal profunctors, an extension of the free finite-product category 2-monad from Cat to Prof, and factorisation systems respectively. We exhibit comparison functors between CAT and each of these new frameworks to show that the distributive laws between the Lawvere theories correspond in a suitable way to distributive laws between their associated finitary monads. The different but equivalent formulations then provide, between them, a framework conducive to generalisation, but also an explicit description of the composite theories arising from distributive laws.

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Eugenia Cheng. Distributive Laws for Lawvere Theories (Invited Talk). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cheng:LIPIcs.CALCO.2021.1,
  author =	{Cheng, Eugenia},
  title =	{{Distributive Laws for Lawvere Theories}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-212-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{211},
  editor =	{Gadducci, Fabio and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.1},
  URN =		{urn:nbn:de:0030-drops-153560},
  doi =		{10.4230/LIPIcs.CALCO.2021.1},
  annote =	{Keywords: Distributive laws, Monads, Lawvere theories}
}

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Distributive Laws for Lawvere Theories (Invited Talk)

Abstract

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