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Model structures on categories of models of type theories

Published online by Cambridge University Press:  28 September 2017

VALERY ISAEV*
Affiliation:
Department of Mathematics and Information Technology, Saint Petersburg Academic University, Saint Petersburg, Russia Email: valery.isaev@gmail.com

Abstract

Models of dependent type theories are contextual categories with some additional structure. We prove that if a theory T has enough structure, then the category T-Mod of its models carries the structure of a model category. We also show that if T has Σ-types, then weak equivalences can be characterized in terms of homotopy categories of models.

Type
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Copyright
Copyright © Cambridge University Press 2017 

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