2 Nov 2000

Per Jacobsen "Categorical theory of relations and quantizations".

The category of relations on A will be defined and shown to be isomorphic to the category of A-A  bi-comodules. We use this isomorphism to define a tensor product of relations by categorization and dualization of the well-known tensor product of bi-modules over rings.
The category of relations has a nontrivial group of symmetries and this leads us to a modification of the usual notion of symmetry for a monoidal category. This modified form of symmetry is a solution of a generalized Yang-Baxter equation. Commutative monoids are defined with respect to a given symmetry and it is shown that commutative monoids in the category of relations are generalized equivalence relations.