Open AccessGraph operations and categorical constructions
Author(s) -
Mati Kilp,
Ulrich Knauer
Publication year - 2001
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.2001.05.04
Subject(s) - coproduct , morphism , categorical variable , functor , mathematics , tensor product , graph , disjoint sets , tensor product of algebras , algebra over a field , pure mathematics , discrete mathematics , tensor product of hilbert spaces , tensor contraction , statistics
Most of the usual binary graph operations from disjoint union up to the complete product are interpreted categorically, using the categories Gra, CGra and EGra. This way it is proved that these categories have coproducts, products and tensor products. As a consequence, it turns out that the respective categories with strong morphisms SGra and SEGra do not admit any of these categorical constructions. It is shown that the functors derived from the respective tensor products and products in Gra, CGra and EGra have right adjoints.