Theorems · Theorem · category theory

CategoryTheory.Limits.map_lift_kernelComparison

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {X Y : C}
  (f : X ⟶ Y) {D : Type u₂} [inst_2 : CategoryTheory.Category.{v₂, u₂} D]
  [inst_3 : CategoryTheory.Limits.HasZeroMorphisms D] (G : CategoryTheory.Functor C D)
  [inst_4 : G.PreservesZeroMorphisms] [inst_5 : CategoryTheory.Limits.HasKernel f]
  [inst_6 : CategoryTheory.Limits.HasKernel (G.map f)] {Z : C} {h : Z ⟶ X}
  (w : CategoryTheory.CategoryStruct.comp h f = 0),
  CategoryTheory.CategoryStruct.comp (G.map (CategoryTheory.Limits.kernel.lift f h w))
      (CategoryTheory.Limits.kernelComparison f G) =
    CategoryTheory.Limits.kernel.lift (G.map f) (G.map h) ⋯

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Kernels

Cited by

1 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Limits.HasKernelCategoryTheory.Limits.HasKernel