License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2020.17
URN: urn:nbn:de:0030-drops-116607
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/11660/
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Cockett, Robin ; Lemay, Jean-Simon Pacaud ; Lucyshyn-Wright, Rory B. B.

Tangent Categories from the Coalgebras of Differential Categories

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LIPIcs-CSL-2020-17.pdf (0.6 MB)

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.

BibTeX - Entry

@InProceedings{cockett_et_al:LIPIcs:2020:11660,
  author =	{Robin Cockett and Jean-Simon Pacaud Lemay and Rory B. B. Lucyshyn-Wright},
  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 =	{Maribel Fern{\'a}ndez and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11660},
  URN =		{urn:nbn:de:0030-drops-116607},
  doi =		{10.4230/LIPIcs.CSL.2020.17},
  annote =	{Keywords: Differential categories, Tangent categories, Coalgebra Modalities}
}

Keywords: Differential categories, Tangent categories, Coalgebra Modalities
Collection: 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)
Issue Date: 2020
Date of publication: 06.01.2020

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