@MISC{Berg08typesare, author = {Benno van den Berg and Richard Garner}, title = {Types are weak ω-groupoids}, year = {2008} }

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Abstract

We define a notion of weak ω-category internal to a model of Martin-Löf 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.