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arXiv · 1607.07407

Model Structures on Categories of Models of Type Theories

Valery Isaev
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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 $T\text{-}\mathbf{Mod}$ of its models carries the structure of a model category. We also show that if $T$ has $\Sigma$ types, then weak equivalences can be characterized in terms of homotopy categories of models.

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Valery Isaev. 2016-07-25. Model Structures on Categories of Models of Type Theories. https://arxiv.org/abs/1607.07407

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