Publication details

Two-dimensional regularity and exactness

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BOURKE John Denis GARNER Richard Henry George

Year of publication 2014
Type Article in Periodical
Magazine / Source Journal of Pure and Applied Algebra
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords 2-category Exactness
Description 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 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.
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