Tuesday, 10 April 2001
2:30 - 4:00    Richard Wood
               Decomposing Regularity

Abstract:
Many important classes of categories are specified by certain types of
colimits, certain types of limits, and exactness conditions relating
these. If the colimits are given by a KZ-doctrine R and the limits by
a co-KZ-doctrine L then it makes sense to enquire about the existence
of a distributive law LR--->RL in the sense of Beck. (Essentially,
there is at most one such law in this context.) Given such a law, an
algebra for the composite doctrine RL is a category C with
        colimits as prescribed by R,
        limits as prescribed by L,
        specification of R-colimits, RC--->C, L-limit-preserving.
Examples will be given. The talk will report on joint work with
Claudia Centazzo directed towards the problem of solving D=RL, for R,
where D is the doctrine for regular categories and L is the doctrine
for categories with finite limits.