Theorems · Theorem · category theory

CategoryTheory.Abelian.imageIsoImage_inv

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {X Y : C} (f : X ⟶ Y),
  (CategoryTheory.Abelian.imageIsoImage f).inv =
    CategoryTheory.Limits.kernel.lift (CategoryTheory.Limits.cokernel.π f) (CategoryTheory.Limits.image.ι f) ⋯

Defined in: Mathlib.CategoryTheory.Abelian.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Iso.invstatement · cited by 6,514
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.Abelianstatement and proof · cited by 1,753
CategoryTheory.Limits.cokernelstatement · cited by 229
CategoryTheory.Limits.cokernel.πstatement and proof · cited by 194
CategoryTheory.Limits.imagestatement and proof · cited by 124
CategoryTheory.Limits.image.ιstatement and proof · cited by 104
CategoryTheory.Limits.MonoFactorisation.Iproof · cited by 83
CategoryTheory.Limits.kernel.liftstatement and proof · cited by 64

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