The coherator \Theta^{\infty}_W of cubical weak \infty-categories with connections

This work exhibits two applications of the combinatorial approach in [۱۲] of the small category \Theta_۰ which objects are cubical pasting diagrams. First we provide an accurate description of the monad \mathbb{S}=(S,\lambda,\mu) acting on the category {\mathbb{C}\mathbb{S}\text{ets}} of cubical sets (without degeneracies and connections), which algebras are cubical strict \infty-categories with connections, and show that this monad is cartesian, which solve a conjecture in \cite{camark-cub}. Secondly we give a precise construction of the cubical coherator \Theta^{\infty}_W which set-models are cubical weak \infty-categories with connections, and we also give a precise construction of the cubical coherator \Theta^{\infty}_{W^{۰}} which set-models are cubical weak \infty-groupoids with connections.

کلیدواژه ها:

Cubical \infty-categories ، cubical coherators ، Grothendieck approach of cubical weak \infty-categories