WEAK ω-CATEGORIES FROM INTENSIONAL TYPE THEORY

We show that for any type in Martin-Löf Intensional Type Theory, the terms of that type and its higher identity types form a weak ω-category in the sense of Leinster. Precisely, we construct a contractible globular operad PMLId of definable “composition laws”, and give an action of this operad on the terms of any type and its identity types.

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