Monomorphisms of group objects #
A morphism of group objects is a monomorphism whenever its underlying morphism is a monomorphism. The faithful forgetful functor reflects monomorphisms, so subobject constructions can use monicity in the ambient category.
@[instance 900]
instance
CategoryTheory.Grp.mono_of_mono_hom
{C : Type u}
[Category.{v, u} C]
[CartesianMonoidalCategory C]
{G H : Grp C}
(f : G ⟶ H)
[Mono f.hom.hom]
:
Mono f
A morphism of group objects is monic if its underlying morphism is monic.