A Type Theory for Strictly Unital ∞-Categories

07/16/2020

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by   Eric Finster, et al.

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We present a type theory for strictly unital ∞-categories, in which a term computes to its strictly unital normal form. Using this as a toy model, we argue that it illustrates important unresolved questions in the foundations of type theory, which we explore. Furthermore, our type theory leads to a new definition of strictly unital ∞-category, which we claim is stronger than any previously described in the literature.