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A category-theoretic version of the identity type weak factorization system
Stockholm University, Faculty of Science, Department of Mathematics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Gambino and Garner proved that the syntactic category of a dependent type theory with identity types can be endowed with a weak factorization system structure, called identity type weak factorization system. In this paper we consider an enrichment of Joyal's notion of tribe which allow us to prove a purely category-theoretic version of the identity type weak factorization system, thus generalizing Gambino and Garner's result. We investigate then how it relates with other well-known weak factorization systems, namely those arising from Quillen model structures on the category of topological spaces and on the category of small groupoids.

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Algebra and Logic
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URN: urn:nbn:se:su:diva-109909OAI: oai:DiVA.org:su-109909DiVA: diva2:769630
Available from: 2014-12-08 Created: 2014-12-01 Last updated: 2017-11-22Bibliographically approved

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CiteExportLink to record
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  • apa
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