pp. 211-226 in
R. Berghammer, A. Jaoua, Bernhard Möller (eds.)
Relations and Kleene Algebra in Computer Science, RelMiCS/AKA 2009,
Doha, Qatar, Nov. 1–5, 2009,
We define collagories essentially as “distributive allegories without zero morphisms”, and show that they are sufficient for accommodating the relation-algebraic approach to graph transformation. Collagories closely correspond to the adhesive categories important for the categorical DPO approach to graph transformation. but thanks to their relation-algebraic flavour provide a more accessible and more flexible setting.
An expanded version of this paper, including detailed proofs, is available as SQRL Report Nr. 56