Dear Michael, You are obviously raising interesting questions. I may have and answer but I dont know! Excuse my ignorance, but I do not understand your language. 1)What is a bicolimit? 2)What is a codescent object? 3)What are the pseudo-monadicity theorems? Best, André -------- Message d'origine-------- De: categories@mta.ca de la part de Michael Shulman Date: lun. 24/05/2010 14:42 À: categories Objet : categories: presentable vs. locally presentable Dear all, I wonder how the following 2-categories are related? 1. The 2-category of locally presentable categories and left adjoints. 2. The full sub-2-category of the 2-category of cocomplete categories and cocontinuous functors, consisting of those categories which are small bicolimits (in that 2-category) of diagrams of presheaf categories on small categories. 3. Like (2), but consisting only of those categories which are codescent objects of diagrams of presheaf categories on small categories. ... [For admin and other information see: http://www.mta.ca/~cat-dist/ ]