Subcategory

In mathematics, specifically category theory, a subcategory of a category ${\displaystyle {\mathcal {C}}}$ is a category ${\displaystyle {\mathcal {S}}}$ whose objects are objects in ${\displaystyle {\mathcal {C}}}$ and whose morphisms are morphisms in ${\displaystyle {\mathcal {C}}}$ with the same identities and composition of morphisms. Intuitively, a subcategory of ${\displaystyle {\mathcal {C}}}$ is a category obtained from ${\displaystyle {\mathcal {C}}}$ by "removing" some of its objects and arrows.