Theorems · Theorem · category theory

CategoryTheory.Limits.imageSubobjectMap_arrow

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {W X Y Z : C} {f : W ⟶ X}
  [inst_1 : CategoryTheory.Limits.HasImage f] {g : Y ⟶ Z} [inst_2 : CategoryTheory.Limits.HasImage g]
  (sq : CategoryTheory.Arrow.mk f ⟶ CategoryTheory.Arrow.mk g) [inst_3 : CategoryTheory.Limits.HasImageMap sq],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.imageSubobjectMap sq)
      (CategoryTheory.Limits.imageSubobject g).arrow =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.imageSubobject f).arrow
      (CategoryTheory.Arrow.Hom.right sq)

Defined in

Mathlib.CategoryTheory.Subobject.Limits

Cited by

2 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasImageCategoryTheory.Limits.HasImageCategoryTheory.Limits.HasImageMap