Theorems · Definition · category theory

CategoryTheory.Limits.cokernelIsoOfEq

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {X Y : C} →
        {f g : X ⟶ Y} →
          [inst_2 : CategoryTheory.Limits.HasCokernel f] →
            [inst_3 : CategoryTheory.Limits.HasCokernel g] →
              f = g → (CategoryTheory.Limits.cokernel f ≅ CategoryTheory.Limits.cokernel g)

If two morphisms are known to be equal, then their cokernels are isomorphic.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Kernels

Cited by

12 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasCokernelCategoryTheory.Limits.HasCokernel