## § Never forget monic again

• Remember monic ~ injective.
• Remember that injective is $f(x) = f(y) \implies x = y$.
• Since we're doing category theory, replace $x$ and $y$ by functions $h(p)$ and $k(p)$.
• This means that the rule of monic is $\forall p, f(h(p)) = f(k(p)) \implies h = k$.
• Thus, monic is left cancellative!