Theorems · Theorem · category theory

CategoryTheory.ConcreteCategory.mono_of_injective

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {FC : C → C → Type u_1} {CC : C → Type w}
  [inst_1 : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)] [inst_2 : CategoryTheory.ConcreteCategory C FC] {X Y : C}
  (f : X ⟶ Y), Function.Injective ⇑(CategoryTheory.ConcreteCategory.hom f) → CategoryTheory.Mono f

In any concrete category, injective morphisms are monomorphisms.

Defined in

Mathlib.CategoryTheory.ConcreteCategory.EpiMono

Cited by

12 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategory