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- Daniel R. Licata, Eric Finster
- CSL-LICS
- 2014

Homotopy type theory is an extension of Martin-Löf type theory with principles inspired by category theory and homotopy theory. With these extensions, type theory can be used to construct proofs of homotopy-theoretic theorems, in a way that is very amenable to computer-checked proofs in proof assistants such as Coq and Agda. In this paper, we give a… (More)

This paper contributes to recent investigations of the use of homotopy type theory to give machine-checked proofs of constructions from homotopy theory. We present a mechanized proof of a result called the Blakers-Massey connectivity theorem, which relates the higher-dimensional loop structures of two spaces sharing a common part (represented by a pushout… (More)

- Steve Awodey, Thierry Coquand, +51 authors Sergei Soloviev
- ArXiv
- 2013

We introduce a dependent type theory whose models are weak {\omega}-categories, generalizing Brunerie's definition of {\omega}-groupoids. Our type theory is based on the definition of {\omega}-categories given by Maltsiniotis, himself inspired by Grothendieck's approach to the definition of {\omega}-groupoids. In this setup, {\omega}-categories are defined… (More)

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