Pseudogroupoids and Commutators
George Janelidze, Maria Cristina Pedicchio · Theory and applications of categories · 2001
ABSTRACT. We develop a new approach to Commutator theory based on the theory of internal categorical structures, especially of so called pseudogroupoids. It is motivated by our previous work on internal categories and groupoids in congruence modular varieties. The purpose of this paper is to develop a new approach to commutator theory. Since J. D. H. Smith [S] introduced the notion of commutator for a pair of congruences in a congruence permutable (=Mal’tsev) variety of universal algebras, there were many attemptsto extend thisnotion to more general varietiesand to simplify it. Accordingly,