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math.CT2021
A Type Theory for Strictly Associative Infinity Categories
Eric Finster, Alex Rice, Jamie Vicary
Many definitions of weak and strict -categories have been proposed. In this paper we present a definition for -categories with strict associators, but which is othe…
cs.LO2021
Types are Internal -Groupoids
Antoine Allioux, Eric Finster, Matthieu Sozeau
By extending type theory with a universe of definitionally associative and unital polynomial monads, we show how to arrive at a definition of opetopic type which is able to encode…
math.CT2021★ 3 cited
Synthetic Spectra via a Monadic and Comonadic Modality
Mitchell Riley, Eric Finster, Daniel R. Licata
We extend Homotopy Type Theory with a novel modality that is simultaneously a monad and a comonad. Because this modality induces a non-trivial endomap on every type, it requires a…