Morphisms can have any of the following properties.
A morphism f :: a -> b
is a:
- monomorphism (or monic) if f ∘ g1 = f ∘ g2 implies g1 = g2 for all morphisms g1, g2 : x → a.
- epimorphism (or epic) if g1 ∘ f = g2 ∘ f implies g1 = g2 for all morphisms g1, g2 : b → x.
- bimorphism if f is both epic and monic.
- isomorphism if there exists a morphism g : b → a such that f ∘ g = 1b and g ∘ f = 1a.[b]