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math.LO2022★ 13 cited
Univalent foundations and the equivalence principle
Benedikt Ahrens, Paige Randall North
In this paper, we explore the 'equivalence principle' (EP): roughly, statements about mathematical objects should be invariant under an appropriate notion of equivalence for the ki…
cs.LO2022
Bicategorical type theory: semantics and syntax
Benedikt Ahrens, Paige Randall North, Niels van der Weide
We develop semantics and syntax for bicategorical type theory. Bicategorical type theory features contexts, types, terms, and directed reductions between terms. This type theory is…