%0 Journal Article
%T Algebraic models of cubical weak higher structures
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Kachour, Camell
%D 2022
%\ 01/01/2022
%V 16
%N 1
%P 189-220
%! Algebraic models of cubical weak higher structures
%K cubical weak ∞-groupoids with connections
%K homology theory
%K homotopy theory
%K computer sciences
%R 10.52547/cgasa.2021.101544
%X In this article we recast some of the results developped in articles [19, 22] but in the setup of cubical geometry. Thus we define a monad on ℂ𝕊ets whose algebras are models of cubical weak ∞-groupoids with connections. In addition, we define a monad on the category ℂ𝕊ets ×ℂ𝕊ets whose algebras are models of cubical weak ∞-functors, and a monad on the category ℂ𝕊ets ×ℂ𝕊ets ×ℂ𝕊ets ×ℂ𝕊ets whose algebras are models of cubical weak ∞-natural transformations.
%U https://cgasa.sbu.ac.ir/article_101544_331b33b547e4eadc6d51fc63f0c9c84c.pdf