Monoid action
= Monoid action
{title2=$M\times A\to A$}
A left monoid action assigns each $m\in M$ a map $a\mapsto m\cdot a$ with $1\cdot a=a$ and $(mn)\cdot a=m\cdot(n\cdot a)$. It need not be invertible or injective. A left <M-set> is equivalently a covariant functor from the one-object category determined by $M$.