algebraic models of cubical weak higher structures

in this article we recast some of the results developped in articles 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.