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• W2964293103 abstract "Connections between homotopy theory and type theory have recently attracted a lot of attention, with Voevodsky’s univalent foundations and the interpretation of Martin-Löf’s identity types in Quillen model categories as some of the highlights. In this article, we establish a connection between a natural weakening of Martin-Löf’s rules for the identity types that has been considered by Cohen, Coquand, Huber and Mörtberg in their work on a constructive interpretation of the univalence axiom on the one hand and the notion of a path category, a slight variation on the classic notion of a category of fibrant objects due to Brown, on the other. This involves showing that the syntactic category associated to a type theory with weak identity types carries the structure of a path category, strengthening earlier results by Avigad, Lumsdaine, and Kapulkin. In this way, we not only relate a well-known concept in homotopy theory with a natural concept in logic but also provide a framework for further developments." @default.
• W2964293103 created "2019-07-30" @default.
• W2964293103 creator A5040167167 @default.
• W2964293103 date "2018-04-30" @default.
• W2964293103 modified "2023-09-27" @default.
• W2964293103 title "Path Categories and Propositional Identity Types" @default.
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• W2964293103 doi "https://doi.org/10.1145/3204492" @default.
• W2964293103 hasPublicationYear "2018" @default.
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