Theorems · Definition · category theory

CategoryTheory.Limits.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) →
                  [G.PreservesZeroMorphisms] →
                    [inst_5 : CategoryTheory.Limits.HasKernel f] →
                      [inst_6 : CategoryTheory.Limits.HasKernel (G.map f)] →
                        G.obj (CategoryTheory.Limits.kernel f) ⟶ CategoryTheory.Limits.kernel (G.map f)

The comparison morphism for the kernel of f. This is an isomorphism iff G preserves the kernel of f; see Mathlib/CategoryTheory/Limits/Preserves/Shapes/Kernels.lean

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Kernels

Cited by

15 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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