Let $\mathscr{A}$ be a category. A map $X \stackrel{f}{\longrightarrow} Y$ in $\mathscr{A}$ is monic (or a monomorphism) if for all objects $A$ and maps $\parpairi{A}{X}{x}{x’}$, \(f \circ x = f \circ x' \implies x = x'.\)