eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-01-06
17:1
17:17
10.4230/LIPIcs.CSL.2020.17
article
Tangent Categories from the Coalgebras of Differential Categories
Cockett, Robin
1
Lemay, Jean-Simon Pacaud
2
Lucyshyn-Wright, Rory B. B.
3
University of Calgary, Department of Computer Science, Canada
University of Oxford, Department of Computer Science, UK
Brandon University, Department of of Mathematics and Computer Science, Canada
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol152-csl2020/LIPIcs.CSL.2020.17/LIPIcs.CSL.2020.17.pdf
Differential categories
Tangent categories
Coalgebra Modalities