Theorems · Theorem · category theory

CategoryTheory.Functor.Faithful.map_injective

∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {D : Type u₂} {inst_1 : CategoryTheory.Category.{v₂, u₂} D}
  {F : CategoryTheory.Functor C D} [self : F.Faithful] {X Y : C}, Function.Injective F.map

F.map is injective for each X Y : C.

Defined in

Mathlib.CategoryTheory.Functor.FullyFaithful

Cited by

3 results in Mathlib

Foundations

Depth 4 from the axioms · uses no axioms

Assumes

CategoryTheory.Functor.Faithful