Limits in free coproduct completions Original Research Article

For a small category C with multilimits for finite diagrams, a conceptual description of its free coproduct completion ∑(C) is given as the category of those set-valued functors of a finitely accessible category with connected limits which preserve these limits and filtered colimits. In this way we recognize the free coproduct completion as a finitely complete category and show that ∑(C) is universal with respect to existence of finite limits and of small coproducts which are disjoint and stable under pullback.