Class operators H S P

Summary

The class operators $H$, $S$ and $P$ act on classes of algebras of one signature. They give the homomorphic images, the subalgebras and the direct products of the members of the class. They are the three closure operations that appear in Birkhoff's characterisation of varieties. Rules for composing them, such as $SH \le HS$ and $PS \le SP$, lead to Tarski's formula $V(K) = HSP(K)$ for the variety generated by a class $K$.