Let $\mathscr{A}$ and $\mathscr{B}$ be categories. A functor $F{\colon}\linebreak[0] \mathscr{A} \to \mathscr{B}$ consists of: 1. a function \(\ob(\mathscr{A}) \to \ob(\mathscr{B}),\) written as $A \mapsto F(A)$;\n2. for each $A, A’ \in \mathscr{A}$, a function \(\mathscr{A}(A, A') \to \mathscr{B}(F(A), F(A')),\) written as $f \mapsto F(f)$, satisfying the following axioms: 1. $F(f’ \circ f) = F(f’) \circ F(f)$ whenever $A \stackrel{f}{\longrightarrow} A’ \stackrel{f’}{\longrightarrow} A’’$ in $\mathscr{A}$;\n2. $F(1A) = 1{F(A)}$ whenever $A \in \mathscr{A}$.