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. McMaster University SQRL Report No. 56 ∗ This research has been supported by the National Science and Engineering Research Council (NSERC), Canada