## arXiv Analytics

### 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.

A type theory for synthetic $\infty$-categories