Prevariety

Summary

A prevariety is a class of algebras of one signature that is closed under isomorphic copies, subalgebras and direct products. Every quasivariety and every variety is a prevariety, but not conversely. The prevariety generated by a class $K$ consists of the algebras that embed into a product of members of $K$. Every prevariety is reflective: each algebra has a best approximation inside the class, as in the reflection onto a variety.