REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: It is proved that the elements of pushouts in a variety of universal algebras have unique normal forms if a variety is represented by a confluent term rewriting system satisfying some additional requirements for its signature and rules. An application of this fact in Grothendieck's descent theory is given. Namely, it is shown that any codescent morphism is effective in varieties of the above-mentioned kind. In particular, this is the case for the varieties of Mal'tsev algebras, idempotent quasigroups, unipotent quasigroups, left Steiner loops, and right Steiner loops.