van den Berg, B. and Moerdijk, I. (2018) Exact completion of path categories and algebraic set theory: Part I: Exact completion of path categories. Journal of Pure and Applied Algebra, 222 (10). pp. 3137-3181. ISSN 0022-4049
Abstract
© 2017 Elsevier B.V. We introduce the notion of a "category with path objects", as a slight strengthening of Kenneth Brown's classical notion of a "category of fibrant objects". We develop the basic properties of such a category and its associated homotopy category. Subsequently, we show how the exact completion of this homotopy category can be obtained as the homotopy category associated to a larger category with path objects, obtained by freely adjoining certain homotopy quotients. In a second part of this paper, we will present an application to models of constructive set theory. Although our work is partly motivated by recent developments in homotopy type theory, this paper is written purely in the language of homotopy theory and category theory, and we do not presuppose any familiarity with type theory on the side of the reader.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 Elsevier. This is an author produced version of a paper subsequently published in Journal of Pure and Applied Algebra. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 16 Feb 2018 10:25 |
Last Modified: | 20 May 2021 15:21 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.jpaa.2017.11.017 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:127387 |