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arXiv · 2303.05623

Relating homotopy equivalences to conservativity in dependent type theories with computation axioms

Matteo Spadetto
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Abstract

We prove a conservativity result for extensional type theories over propositional ones, i.e. dependent type theories with propositional computation rules, or computation axioms, using insights from homotopy type theory. The argument exploits a notion of canonical homotopy equivalence between contexts, and uses the notion of a category with attributes 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.

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BibTeXRIS

Matteo Spadetto. 2023-03-09. Relating homotopy equivalences to conservativity in dependent type theories with computation axioms. https://doi.org/10.46298/lmcs-21(3%3A32)2025

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