Theorems · Definition · category theory

CategoryTheory.equivalenceReflectsNormalMono

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {D : Type u₂} →
        [inst_2 : CategoryTheory.Category.{v₁, u₂} D] →
          [inst_3 : CategoryTheory.Limits.HasZeroMorphisms D] →
            (F : CategoryTheory.Functor C D) →
              [F.IsEquivalence] →
                {X Y : C} → {f : X ⟶ Y} → CategoryTheory.NormalMono (F.map f) → CategoryTheory.NormalMono f

If F is an equivalence and F.map f is a normal mono, then f is a normal mono.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic

Cited by

0 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.IsEquivalence