Types are weak ω-groupoids

Benno Van Den Berg; Richard Garner

doi:10.1112/plms/pdq026

Types are weak ω-groupoids

Benno Van Den Berg^*, Richard Garner

^*Corresponding author for this work

Research output: Contribution to journal › Article

46 Citations (Scopus)

Abstract

We define a notion of weak ω-category internal to a model of Martin-Löf's type theory, and prove that each type bears a canonical weak ω-category structure obtained from the tower of iterated identity types over that type. We show that the ω-categories arising in this way are in fact ω-groupoids.

Original language	English
Pages (from-to)	370-394
Number of pages	25
Journal	Proceedings of the London Mathematical Society
Volume	102
Issue number	2
DOIs	https://doi.org/10.1112/plms/pdq026
Publication status	Published - Feb 2011
Externally published	Yes

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AB - We define a notion of weak ω-category internal to a model of Martin-Löf's type theory, and prove that each type bears a canonical weak ω-category structure obtained from the tower of iterated identity types over that type. We show that the ω-categories arising in this way are in fact ω-groupoids.

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