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math.CT2024
Invertible cells in -categories
Thibaut Benjamin, Ioannis Markakis
We study coinductive invertibility of cells in weak -categories. We use the inductive presentation of weak -categories via an adjunction with the category of computads, and s…
math.CT2024★ 2 cited
CaTT contexts are finite computads
Thibaut Benjamin, Ioannis Markakis, Chiara Sarti
Two novel descriptions of weak ω-categories have been recently proposed, using type-theoretic ideas. The first one is the dependent type theory CaTT whose models are ω-categories.…
math.CT2024★ 1 cited
Hom -categories of a computad are free
Thibaut Benjamin, Ioannis Markakis
We provide a new description of the hom functor on weak -categories, and we show that it admits a left adjoint that we call the suspension functor. We then show that the hom fun…