12 Mar
1992
12 Mar
'92
7:46 p.m.
Diers' notion of multi-adjoint includes a uniqueness so that algebraically closed fields^op is not an example. Essentially, it is that there is an initial object in each component, so it follows by definition. You are probably right about Joyal's claim, but it is even easier to see that if regepis are closed under composition (implied by pullback stability), then every strong epi is regular. Oh well, I guess my memory was faulty. What are wide pullbacks? How can pullback preservation imply anything about filtered colimits? In any case, it is easy to find limit preserving underlying functors that don't preserve filtered colimits. Michael =====================================================================