  The family of Weisfeiler-Leman equivalences on graphs is a widely studied
approximation of graph isomorphism with many different characterizations. We
study these, and other approximations of isomorphism defined in terms of
refinement operators and Schurian Polynomial Approximation Schemes (SPAS). The
general framework of SPAS allows us to study a number of parameters of the
refinement operators based on Weisfeiler-Leman refinement, logic with counting,
lifts of Weisfeiler-Leman as defined by Evdokimov and Ponomarenko, and the
invertible map test introduced by Dawar and Holm, and variations of these, and
establish relationships between them.
