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The homotopy theory of type theories
University of Western Ontario.
Stockholm University, Faculty of Science, Department of Mathematics. (Logik)ORCID iD: 0000-0003-1390-2970
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We construct a left semi-model structure on the category of intensional type theories (precisely, on CxlCat_{Id,1,Σ(,Πext)}). This presents an infinity-category of such type theories; we show moreover that there is an infinity-functor Cl_∞ from there to the infinity-category of suitably structured quasi-categories. This allows a precise formulation of the conjectures that intensional type theory gives internal languages for higher categories, and provides a framework and toolbox for further progress on these conjectures.

National Category
Algebra and Logic
Research subject
Mathematical Logic
Identifiers
URN: urn:nbn:se:su:diva-140148OAI: oai:DiVA.org:su-140148DiVA: diva2:1077743
Available from: 2017-02-28 Created: 2017-02-28 Last updated: 2017-02-28

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Lumsdaine, Peter LeFanu
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