Factorisation and Cohomology of Higher Categories
Scott Balchin
TL;DR
This paper introduces a method to factorize small strict n-categories into 1-categories, extends the theory to include many $ $-categories, and uses this to define cohomology theories for higher categories.
Contribution
It presents a novel iterative factorization approach for higher categories and develops a cohomology framework based on this factorization.
Findings
Unique factorization of small strict n-categories into 1-categories
Extension of factorization to a broad class of $ $-categories
Concrete examples of factorisations in low-dimensional 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 -categories. We use this factorisation to define cohomology theory for higher categories. Finally, we discuss some concrete examples of factorisations of low dimensional categories.
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Taxonomy
TopicsAdvanced Algebra and Logic · graph theory and CDMA systems · Rings, Modules, and Algebras