Small category (category theory)

In category theory, a small category is one with no more than a set's worth of morphisms (c.f. Russel's paradox). for a small category $𝐂$, there exist functions

• $\text{Dom}:\text{Mor}𝐂\to \text{Ob}𝐂$, mapping each morphism to its domain. I.e., every $f:A\to B$ is sent to $A$.

• $\text{Cod}:\text{Mor}𝐂\to \text{Ob}𝐂$, mapping morphisms to their codomains. I.e., every $f:A\to B$ to $B$.

• X \mapsto \id{X} : \Ob\;\C{C} \to \Mor\;\C{C} ParseError: Function "\id" is not trusted at position 11: X \mapsto \̲i̲d̲{X} : \Ob\;\C{C…, a bijection mapping each object to its identity morphism.