### arXiv:1804.05045 [math.CT]AbstractReferencesReviewsResources

#### Morita equivalences between algebraic dependent type theories

Published 2018-04-13Version 1

We define a notion of equivalence between algebraic dependent type theories which we call Morita equivalence. This notion has a simple syntactic description and an equivalent description in terms of models of the theories. The category of models of a type theory often carries a natural structure of a model category. If this holds for the categories of models of two theories, then a map between them is a Morita equivalence if and only if the adjunction generated by it is a Quillen equivalence.

**Comments:**32 pages

arXiv:1705.07442 [math.CT] (Published 2017-05-21)

A type theory for synthetic $\infty$-categories

arXiv:1704.04747 [math.CT] (Published 2017-04-16)

Dependent Cartesian Closed Categories

arXiv:1507.02648 [math.CT] (Published 2015-07-09)

Locally Cartesian Closed Quasicategories from Type Theory