2017/02/01 by Camell Kachour, Kachour, Camell · 1 citation
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.1702.00336
In this article we show how to build main aspects of our paper on globular weak (∞,n)-categories, but now for the cubical geometry. Thus we define a monad on the category ℂ\mathbbSets of cubical sets which algebras are models of cubical weak ∞-categories. Also for each n∈ℕ we define a monad on ℂ\mathbbSets which algebras are models of cubical weak (∞,n)-categories. And finally we define a monad on the category ℂ\mathbbSets2 which algebras are models of cubical weak ∞-functors, and a monad on the category ℂ\mathbbSets4 which algebras are models of cubical weak natural ∞-transformations.