Theorems · Theorem · category theory

CategoryTheory.Limits.imageSubobject_iso_comp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} [CategoryTheory.Limits.HasEqualizers C] {X' : C}
  (h : X' ⟶ X) [inst_2 : CategoryTheory.IsIso h] (f : X ⟶ Y) [inst_3 : CategoryTheory.Limits.HasImage f],
  CategoryTheory.Limits.imageSubobject (CategoryTheory.CategoryStruct.comp h f) = CategoryTheory.Limits.imageSubobject f

Precomposing by an isomorphism does not change the image subobject.

Defined in

Mathlib.CategoryTheory.Subobject.Limits

Cited by

2 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasEqualizersCategoryTheory.IsIsoCategoryTheory.Limits.HasImage