Semigroups

In the setting of Routine Facts, Continued: Typed Arithmetic, Maps and Predicativity, let $S$ be a set and let $\cdot$ be a binary operation on $S$.

(i) Semigroups. The pair $(S,\cdot)$ is a semigroup if $\cdot$ is associative. For $s,t\in S$ the value $s\cdot t$ of Binary Operations on a Set (ii) is also written $st$.