TY - JOUR
ID - 104139
TI - The coherator $\Theta^{\infty}_W$ of cubical weak $\infty$-categories with connections
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Kachour, Camell
AD - Laboratoire de Math\'ematiques d'Orsay, UMR 8628,
Universit\'e de Paris-Saclay and CNRS,
B\^atiment 307, Facult\'e des Sciences d'Orsay,
94015 ORSAY Cedex, France.
Y1 - 2024
PY - 2024
VL - 21
IS - 1
SP - 69
EP - 126
KW - Cubical $\infty$-categories
KW - cubical coherators
KW - Grothendieck approach of cubical weak $\infty$-categories
DO - 10.48308/cgasa.2023.104139
N2 - This work exhibits two applications of the combinatorial approach in [12] of the small category $\Theta_0$ 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 $\Theta^{\infty}_{W^{0}}$ which set-models are cubical weak $\infty$-groupoids with connections.
UR - https://cgasa.sbu.ac.ir/article_104139.html
L1 - https://cgasa.sbu.ac.ir/article_104139_624697552a25e8bee0393e08ecf9ddf6.pdf
ER -