Types are weak ω-groupoids

Benno Van Den Berg*, Richard Garner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

67 Citations (Scopus)


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 languageEnglish
Pages (from-to)370-394
Number of pages25
JournalProceedings of the London Mathematical Society
Issue number2
Publication statusPublished - Feb 2011
Externally publishedYes


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