Theorems · Definition · category theory

CategoryTheory.Limits.image.eqToIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y : C} →
      {f f' : X ⟶ Y} →
        [inst_1 : CategoryTheory.Limits.HasImage f] →
          [inst_2 : CategoryTheory.Limits.HasImage f'] →
            f = f' → (CategoryTheory.Limits.image f ≅ CategoryTheory.Limits.image f')

An equation between morphisms gives an isomorphism between the images.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Images

Cited by

3 results in Mathlib

Foundations

Depth 12 from the axioms · uses propext, Classical.choice

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasImageCategoryTheory.Limits.HasImage