6 citations · 14 across the 8 of their papers we have counts for
5 papers · 1 filter
Contextually indexed contextual categories
Valery Isaev
In this paper, we define a generalization of indexed categories and contextual categories which we call contextually indexed (contextual) categories. While contextual categories ar…
Indexed type theories
Valery Isaev
In this paper, we define indexed type theories which are related to indexed (-)categories in the same way as (homotopy) type theories are related to (-)categories.…
Model category of marked objects
Valery Isaev
For every functor , where is a small category and is a model category which satisfies some mild hypotheses, we…
Model Structures on Categories of Models of Type Theories
Valery Isaev
Models of dependent type theories are contextual categories with some additional structure. We prove that if a theory has enough structure, then the category $T\text{-}\mathbf{…
On fibrant objects in model categories
Valery Isaev
In this paper, we study properties of maps between fibrant objects in model categories. We give a characterization of weak equivalences between fibrant object. If every object of a…