A category is cocomplete if it has all small colimits: that is, if every small diagram where is a small category has a colimit in . Equivalently, a category is cocomplete if it has all small wide pushouts and an initial object. The most natural morphisms between cocomplete categories are the cocontinuous functors. A category is cocomplete if and only if it has small coproducts and reflexive coequalisers. Dually, a category with all small limits is a complete category. A category is cocomplete...