A factorization of regularity

[摘要] Earlier, the authors showed that categories with regular factorizations (in the sense, of Kelly) and with regular epimorphisms closed under composition, are algebras for a KZ-doctrine R on the 2-category cat(ker), of all categories and functors which preserve kernel inclusions. Here we show that the usual 2-category lex, of categories with finite limits and left exact functors, is cat(ker)(L), the 2-category of algebras for a coKZ-doctrine Y on cat(ker). Combined with our earlier results this shows that the 2-category reg, of regular categories and regular functors, is the 2-category of algebras for a distributive law LR -> RL over the 2-category cat(ker). (c) 2005 Elsevier B.V. All rights reserved.

[发布日期] 2005-12-01