Endomorphism

category-theory

Definition

Endomorphism

Let $\mathcal{C}$ be a category and let $X$ be an object of $\mathcal{C}$.

A endomorphism of $X$ is a morphism

$$f:X\to X$$

in $\mathcal{C}$.

The set of all endomorphisms of $X$ in $\mathcal{C}$ is usually denoted

$${\mathrm{End}}_{\mathcal{C}}(X)={\mathrm{Hom}}_{\mathcal{C}}(X,X).$$