A functor $F{\colon}\linebreak[0] \mathscr{A} \to \mathscr{B}$ is faithful (respectively, full) if for each $A, A’ \in \mathscr{A}$, the function \(\begin{array}{ccc} \mathscr{A}(A, A') &\to &\mathscr{B}(F(A), F(A')) \\ f &\mapsto &F(f) \end{array}\) is injective (respectively, surjective).