Factorisation and Cohomology of Higher Categories

Abstract

We construct an iterative method for factorising small strict n-categories into a unique (up to isomorphism) collection of small 1- categories. Following this we develop the theory to include a large class of $\infty$-categories. We use this factorisation to define cohomology theory for higher categories. Finally, we discuss some concrete examples of factorisations of low dimensional categories.

14 pages, 3 figures