mathlib3 documentation


Monomorphisms in Module R #

THIS FILE IS SYNCHRONIZED WITH MATHLIB4. Any changes to this file require a corresponding PR to mathlib4.

This file shows that an R-linear map is a monomorphism in the category of R-modules if and only if it is injective, and similarly an epimorphism if and only if it is surjective.

theorem Module.ker_eq_bot_of_mono {R : Type u} [ring R] {X Y : Module R} (f : X Y) [category_theory.mono f] :
theorem Module.range_eq_top_of_epi {R : Type u} [ring R] {X Y : Module R} (f : X Y) [category_theory.epi f] :
def Module.unique_of_epi_zero {R : Type u} [ring R] {M : Type v} [add_comm_group M] [module R M] (X : Module R) [h : category_theory.epi 0] :

If the zero morphism is an epi then the codomain is trivial.

@[protected, instance]
@[protected, instance]