Two-dimensional regularity and exactness |
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Authors: | John Bourke Richard Garner |
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Affiliation: | 1. Department of Mathematics and Statistics, Masaryk University, Kotlá?ská 2, Brno 60000, Czech Republic;2. Department of Mathematics, Macquarie University, NSW 2109, Australia |
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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 and . |
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Keywords: | 18F10 18A32 18D05 |
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