Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4596205 | Journal of Pure and Applied Algebra | 2014 | 26 Pages |
Abstract
We define notions of regularity and (Barr-)exactness for 2-categories. In fact, we define three notions of regularity and exactness, each based on one of the three canonical ways of factorising a functor in Cat: as (surjective on objects, injective on objects and fully faithful), as (bijective on objects, fully faithful), and as (bijective on objects and full, faithful). The correctness of our notions is justified using the theory of lex colimits [12] introduced by Lack and the second author. Along the way, we develop an abstract theory of regularity and exactness relative to a kernel–quotient factorisation, extending earlier work of Street and others [24] and [3].
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
John Bourke, Richard Garner,