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arXiv · 1205.5527

Combinatorial realizability models of type theory

Pieter Hofstra·Michael A. Warren
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Abstract

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 syntactic model with a notion of realizability; it also encompasses the well-known Hofmann- Streicher groupoid semantics. As our main application, we use the model to analyse the syntactic groupoid associated to the type theory generated by a graph G, showing that it has the same homotopy type as the free groupoid generated by G.

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Pieter Hofstra, Michael A. Warren. 2012-05-24. Combinatorial realizability models of type theory. https://arxiv.org/abs/1205.5527

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