Dear All The Fundamental Theorem of Category Theory, to my mind, encompasses all the facts surrounding the fact that the presheaf category PA is the bicategorically free small-cocompletion of a small category A. With my students I have always called it: "The Whole Kan Business". It can be expressed something like this: Theorem. For each small category A and small-cocomplete category X, left Kan extension along the Yoneda embedding y_A : A --> PA provides an equivalence of categories [A,X] --> Cocts[PA,X] where the codomain is the full subcategory of the functor category [PA,X] consisting of the small-colimit-preserving functors. Moreover, the value of the equivalence at j : A --> X has a right adjoint given by x |--> X(j-,x). Ross [For admin and other information see: http://www.mta.ca/~cat-dist/ ]