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math.LO2012
Combinatorial realizability models of type theory
Pieter Hofstra, Michael A. Warren
We introduce a new model construction for Martin-Löf intensional type theory, which is sound and complete for the 1-truncated version of the theory. The model formally combines the…
math.LO2009
Martin-Löf Complexes
Steve Awodey, Pieter Hofstra, Michael A. Warren
In this paper we define Martin-Löf complexes to be algebras for monads on the category of (reflexive) globular sets which freely add cells in accordance with the rules of intension…