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math.CT2022★ 2 cited
On the -topos semantics of homotopy type theory
Emily Riehl
Many introductions to homotopy type theory and the univalence axiom gloss over the semantics of this new formal system in traditional set-based foundations. This expository article…
math.CT2022★ 3 cited
Classifying topoi in synthetic guarded domain theory
Daniele Palombi, Jonathan Sterling
Several different topoi have played an important role in the development and applications of synthetic guarded domain theory (SGDT), a new kind of synthetic domain theory that abst…
math.CT2022
Strict universes for Grothendieck topoi
Daniel Gratzer, Michael Shulman, Jonathan Sterling
Hofmann and Streicher famously showed how to lift Grothendieck universes into presheaf topoi, and Streicher has extended their result to the case of sheaf topoi by sheafification.…