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Morita equivalences between algebraic dependent type theories (1804.05045v2)
Published 13 Apr 2018 in math.CT, cs.LO, and math.LO
Abstract: 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.
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