A conservativity result for homotopy elementary types in dependent type theory

03/09/2023

∙

by   Matteo Spadetto, et al.

∙

0

∙

share

We prove a conservativity result for extensional type theories over propositional ones, i.e. dependent type theories with propositional computation rules, using insights from homotopy type theory. The argument exploits a notion of canonical homotopy equivalence between contexts, and uses the notion of a type-category to phrase the semantics of theories of dependent types. Informally, our main result asserts that, for judgements essentially concerning h-sets, reasoning with extensional or propositional type theories is equivalent.