In a standard 2-category, every homset C(A,B) is a category. In C we have structures like: f A, B in C ---------------> f, g : A --> B || A || s B s : f ==> g \/ ---------------> g What I need is a structure which resembles a 2-category, but in which the _union_ of all homsets is a category. In such a category we have structures like: f A, B, A', B' in C A ---------------> B f : A --> B || g : A' --> B' || s s : f ==> g \/ A' ---------------> B' g and we have horizontal and vertical composition which satisfy the interchange law (s . s') o (t . t') = (s o t) . (s' o t'), 2-functors etc. I would like to know if such a structure has been explored, if it has a name, and references to papers describing it. -- Nico Verwer | verwer@cs.ruu.nl Dept. of Computer Science, University of Utrecht | +31 30 533921 p.o. box 80.089 3508 TB Utrecht The Netherlands