Dear Uwe, Of course, Rel is self-dual, as you already remarked. Consider a relation R from A to B, i.e., a subset of A x B. Define the image-function img(R) from the powerset P(A) to the powerset P(B) by mapping a subset U of A to the union of all subsets of B of the form aR with a in U (where aR consists of all elements in B R-related to a). Then R is a monomorphism in Rel iff img(R) is injective, which in particular implies that R is total. Dually, R is an epimorphism in Rel iff img(R^op) is injective, in particular R^op then is total. Moreover, disjoint unions serve as both coproducts and products in Rel, but (co)equalizers in general fail to exist. Best regards, -- Jürgen Koslowski [For admin and other information see: http://www.mta.ca/~cat-dist/ ]