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DOI: 10.4230/LIPIcs.CSL.2020.17

Tangent Categories from the Coalgebras of Differential Categories

Authors: Robin Cockett, Jean-Simon Pacaud Lemay, and Rory B. B. Lucyshyn-Wright

Published in: LIPIcs, Volume 152, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)

Abstract

Following the pattern from linear logic, the coKleisli category of a differential category is a Cartesian differential category. What then is the coEilenberg-Moore category of a differential category? The answer is a tangent category! A key example arises from the opposite of the category of Abelian groups with the free exponential modality. The coEilenberg-Moore category, in this case, is the opposite of the category of commutative rings. That the latter is a tangent category captures a fundamental aspect of both algebraic geometry and Synthetic Differential Geometry. The general result applies when there are no negatives and thus encompasses examples arising from combinatorics and computer science.

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Robin Cockett, Jean-Simon Pacaud Lemay, and Rory B. B. Lucyshyn-Wright. Tangent Categories from the Coalgebras of Differential Categories. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cockett_et_al:LIPIcs.CSL.2020.17,
  author =	{Cockett, Robin and Lemay, Jean-Simon Pacaud and Lucyshyn-Wright, Rory B. B.},
  title =	{{Tangent Categories from the Coalgebras of Differential Categories}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Fern\'{a}ndez, Maribel and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2020.17},
  URN =		{urn:nbn:de:0030-drops-116607},
  doi =		{10.4230/LIPIcs.CSL.2020.17},
  annote =	{Keywords: Differential categories, Tangent categories, Coalgebra Modalities}
}

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Documents authored by Lucyshyn-Wright, Rory B. B.

Tangent Categories from the Coalgebras of Differential Categories

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