Malcev variety
Todd Trimble
A Malcev operation on a set is a ternary operation, a function
which satisfies the identities and . An important motivating example is the operation of a heap, for example the operation on a group defined by .
An algebraic theory is a Malcev theory when contains a Malcev operation. An algebraic theory is Malcev iff one of the following equivalent statements is true:
in the category of -algebras, every internal reflexive relation is a congruence;
in the category of -algebras, the composite (as...