The idea of ``summing over all intermediate states{''} that is central for implementing locality in quantum systems can be realized by coend constructions. In the concrete case of systems of conformal blocks for a certain class of conformal vertex algebras, one deals with coends in functor categories. Working with these coends involves quite a few subtleties which, even though they have in principle already been understood twenty years ago in papers by Lyubashenko, have not been sufficiently appreciated by the conformal field theory community.