# Category:Examples of Subsemigroups

Let $\struct {S, \circ}$ be an algebraic structure.
Let $T \subseteq S$ such that $\struct {T, \circ {\restriction_T} }$, where $\circ {\restriction_T}$ is the restriction of $\circ$ to $T$, is a semigroup.
Then $\struct {T, \circ {\restriction_T} }$ is a subsemigroup of $S$.