Category

A category \(\mathcal{C}\) consists of

1. A class of objects, \(\mathrm{Ob}(\mathcal{C})\)
2. for objects \(A,B \in \mathrm{Ob}(\mathcal{C})\) a class of morphisms \(\mathrm{Hom}_{\mathcal{C}}(A,B)\)
3. for each object \(A \in \mathrm{Ob}(\mathcal{C})\) an identity morphism \(\mathrm{id}_{A} \in \mathrm{Hom}_{\mathcal{C}}(A,A)\)
4. A composition of morphisms