6 Nov 14:39 2006

### reflexive coequalizers

Jiri Adamek <adamek <at> iti.cs.tu-bs.de>

2006-11-06 13:39:47 GMT

2006-11-06 13:39:47 GMT

The indiscrete-category functor I: Set -> Cat is not algebraically exact as I claimed in my posting of October 9. But I is a full codomain restriction of one: as in that posting, let F be the forgetful functor the Gabriel-Ulmer theory T of categories to the theory of sets. Then Alg F is an algebraically exact functor from Set to Alg T, and the Yoneda embedding Y: Cat -> Alg T is fully faithful (since the dual of T is dense in Cat). It is easy to see that Alg F is naturally isomorphic to Y.I , thus, I preserves sifted colimits. xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx alternative e-mail address (in case reply key does not work): J.Adamek <at> tu-bs.de xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx