Theorems · Definition · category theory

CategoryTheory.Limits.kernel.mapIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {X Y : C} →
        (f : X ⟶ Y) →
          [inst_2 : CategoryTheory.Limits.HasKernel f] →
            {X' Y' : C} →
              (f' : X' ⟶ Y') →
                [inst_3 : CategoryTheory.Limits.HasKernel f'] →
                  (p : X ≅ X') →
                    (q : Y ≅ Y') →
                      CategoryTheory.CategoryStruct.comp f q.hom = CategoryTheory.CategoryStruct.comp p.hom f' →
                        (CategoryTheory.Limits.kernel f ≅ CategoryTheory.Limits.kernel f')

A commuting square of isomorphisms induces an isomorphism of kernels.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Kernels

Cited by

3 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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