Categorical constructions and adjoint functors on graph categories
by
Ulrich Knauer
Carl von Ossietzky Universität Oldenburg

Most of the usual binary graph operations from disjoint union up to the complete product are interpreted categorically, using the categories Gra, CGra and Grae which denote graphs with different morphisms. This way it is proved that these categories have coproducts, amalgamated coproducts, products and tensor products. As a consequence it turns out that the respective categories with strong morphisms SGra and SGrae do not admit any of these categorial constructions. Moreover, the box, cross and box-cross functors derived from the respective products have right adjoints with respect to the category Gra of graphs with ordinary graph homomorphisms. They are obtained by three new graph compositions.

Date received: January 30, 2001