Algebraic Models of Cubical Weak Higher Structures

In this article we recast some of the results developped in articles [۱۹, ۲۲] 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.

کلیدواژه ها:

cubical weak  ∞-groupoids with connections ، homology theory ، homotopy theory ، computer sciences