We establish sufficient and necessary conditions for a natural sink to be a colimit in DCPO. Based on these conditions we show how to construct a colimit for any functor F from a small category „ into the category DCPO. This demonstrates that the category DCPO is cocomplete. We also investigate under what conditions the colimit object is algebraic. 0 Introduction Colimits play an important role...

We prove cocompleteness of the category of CASL signatures , of monotone signatures, of strongly regular signatures and of strongly locally ltered signatures. This shows that using these signature categories is compatible with a pushout or colimit based module system.

Assuming only a very rudimentary knowledge of enriched category theory — V-categories, V-functors, and V-natural transformations for a closed, symmetric monoidal, complete and cocomplete category V — we introduce weighted limits and colimits, the appropriate sort of limits for the enriched setting. This “modern” approach was introduced to the author through talks by Mike Shulman at the Category...

These notes were written to accompany two talks given in the Algebraic Topology and Category Theory Proseminar at the University of Chicago in Winter 2009. When a category has some notion of limits and colimits associated to it, its ordinary limits and colimits are not necessarily homotopically meaningful. We describe a notion of a “homotopy colimit” for two sorts of categories with a homotopy ...