Dear all, In a current project we have the following situation. For a category we are attempting to define, we know what the objects are, and also the morphisms. Unfortunately we do not have an obvious composition operation. What we do have is a "colimit" operation, which operates on a directed graph labelled by our objects and morphisms, and returns a putative colimit object equipped with a family of morphisms in the usual way (or fails.) We then define the composite of morphisms A->B, B->C to be the colimit of the diagram A->B->C. We then check that this composition operation satisfies the axioms of a category, and that our earlier colimit construction is indeed an actual colimit with respect to the compositional structure. It seems that everything works fine, and we are happy. My question is whether this has any precedent in the literature. The situation as I have described it is a bit simplified, in reality there is some higher categorical stuff going on. Personally I'm sure I've read similar things in the literature in the past but I can't track them down now that I actually need them. The nLab article on "composition" has some stuff about this with regard to transfinite composition, but we're not trying to do anything transfinite here. Best wishes, Jamie ---------- You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. Leave group: https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=leave&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27