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Mathematics > Category Theory

arXiv:1804.08585 (math)
[Submitted on 23 Apr 2018 (v1), last revised 27 Apr 2020 (this version, v3)]

Title:On the local cartesian closure of exact completions

Authors:Jacopo Emmenegger
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Abstract:This paper presents a necessary and sufficient condition on a category with weak finite limits for its exact completion to be (locally) cartesian closed. A paper by Carboni and Rosolini already claimed such a characterisation using a different property on the base category, but we shall show that weak finite limits are not enough for their proof to go through. We shall also indicate how to strengthen the hypothesis for that proof to work. It will become clear that, in the case of ex/lex completions, their characterisation is still valid and it coincides with the one presented here.
Comments: v1: 15 pages. v3: 21 pages, results are unchanged but the presentation has been completely revised. Accepted on J. Pure Appl. Algebra. v4: 20 pages, final journal version
Subjects: Category Theory (math.CT)
MSC classes: (2020) 18D15, 18E08, 18A35, 18B15, 18E20
Cite as: arXiv:1804.08585 [math.CT]
  (or arXiv:1804.08585v3 [math.CT] for this version)
  https://doi.org/10.48550/arXiv.1804.08585
Journal reference: J. Pure Appl. Algebra 224 (2020)
Related DOI: https://doi.org/10.1016/j.jpaa.2020.106414

Submission history

From: Jacopo Emmenegger [view email]
[v1] Mon, 23 Apr 2018 17:23:58 UTC (17 KB)
[v2] Thu, 19 Sep 2019 20:53:46 UTC (28 KB)
[v3] Mon, 27 Apr 2020 10:29:07 UTC (26 KB)
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