Theorems · Definition · category theory

CategoryTheory.Abelian.coimageImageComparisonFunctor

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      [CategoryTheory.Limits.HasKernels C] →
        [CategoryTheory.Limits.HasCokernels C] →
          CategoryTheory.Functor (CategoryTheory.Arrow C) (CategoryTheory.Arrow C)

The coimage-image comparison morphism is functorial.

Defined in: Mathlib.CategoryTheory.Abelian.Images
Cited by: 2 results in Mathlib
Foundations: Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasKernels CategoryTheory.Limits.HasCokernels

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Cites17

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homproof · cited by 32,603
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Arrowstatement and proof · cited by 713
CategoryTheory.Arrow.mkproof · cited by 421
CategoryTheory.Arrow.homproof · cited by 335
CategoryTheory.Limits.kernel.ιproof · cited by 214
CategoryTheory.Limits.cokernel.πproof · cited by 194
CategoryTheory.Arrow.Hom.rightproof · cited by 176
CategoryTheory.Arrow.Hom.leftproof · cited by 160
CategoryTheory.Limits.HasKernelsstatement and proof · cited by 67

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.Abelian.coimageImageComparisonFunctor_mapstatement and proof · cited by 0
CategoryTheory.Abelian.coimageImageComparisonFunctor_objstatement and proof · cited by 0