Theorems · Theorem · category theory

CategoryTheory.Limits.kernelSubobjectMap_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] {X' Y' : C} {f' : X' ⟶ Y'}
  [inst_3 : CategoryTheory.Limits.HasKernel f'] (sq : CategoryTheory.Arrow.mk f ⟶ CategoryTheory.Arrow.mk f') {Z : C}
  (h : X' ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernelSubobjectMap sq)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernelSubobject f').arrow h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernelSubobject f).arrow
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Arrow.Hom.left sq) h)

Defined in

Mathlib.CategoryTheory.Subobject.Limits

Cited by

1 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasKernelCategoryTheory.Limits.HasKernel