Category

definitioncategory-theory

Definition

A category $\mathrm{C}$ is a structure comprised of two classes: $\mathrm{Obj}(\mathrm{C})$, the objects of $\mathrm{C}$, and $\mathrm{Hom}(\mathrm{C})$, the morphisms between all objects in $\mathrm{Obj}(\mathrm{C})$, along with the operation $\circ$ which is composition of morphisms,

$$\circ :\mathrm{Hom}(b,c)\times \mathrm{Hom}(a,b)\mapsto \mathrm{Hom}(a,c),$$

which follows two axioms, 1)

Examples