Theorems · Theorem · category theory

CategoryTheory.Limits.kernel_map_comp_kernelSubobjectIso_inv_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 : CategoryTheory.Subobject.underlying.obj (CategoryTheory.Limits.kernelSubobject f') ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernel.map f f' sq.left sq.right ⋯)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernelSubobjectIso f').inv h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernelSubobjectIso f).inv
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernelSubobjectMap sq) h)

Defined in

Mathlib.CategoryTheory.Subobject.Limits

Cited by

0 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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