Theorems · Theorem · category theory

CategoryTheory.Limits.kernelSubobject_arrow_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  (f : X ⟶ Y) [inst_2 : CategoryTheory.Limits.HasKernel f] {Z : C} (h : X ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernelSubobjectIso f).hom
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernel.ι f) h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernelSubobject f).arrow h

Defined in: Mathlib.CategoryTheory.Subobject.Limits
Cited by: 2 results in Mathlib
Foundations: Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasKernel

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Cites16

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.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Iso.homstatement and proof · cited by 7,684
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Subobjectstatement · cited by 385
CategoryTheory.Limits.kernelstatement · cited by 272
CategoryTheory.Limits.kernel.ιstatement and proof · cited by 214
CategoryTheory.Subobject.underlyingstatement · cited by 211
CategoryTheory.Subobject.arrowstatement and proof · cited by 175

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.kernelSubobjectIsoComp_inv_arrowproof · cited by 1
CategoryTheory.Limits.kernelSubobjectIsoComp_hom_arrowproof · cited by 0