Frame coreflection of a preframe monoid
= Frame coreflection of a preframe monoid
{title2=$R(M)=\{x:e\leq x,\ x*x=x\}$}
For a commutative <monoid object> $(M,*,e)$ in <preframes>, the indicated subset is a <frame>. Its bottom is $e$, its binary join is $*$, and its directed joins and finite meets are inherited. Every homomorphism from a <frame> regarded as a join monoid factors uniquely through this subset. This gives a <coreflective subcategory>.