Theorems · Definition · category theory

CategoryTheory.Limits.isKernelCompMono

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {X Y : C} →
        {f : X ⟶ Y} →
          {c : CategoryTheory.Limits.KernelFork f} →
            CategoryTheory.Limits.IsLimit c →
              {Z : C} →
                (g : Y ⟶ Z) →
                  [hg : CategoryTheory.Mono g] →
                    {h : X ⟶ Z} →
                      (hh : h = CategoryTheory.CategoryStruct.comp f g) →
                        CategoryTheory.Limits.IsLimit
                          (CategoryTheory.Limits.KernelFork.ofι (CategoryTheory.Limits.Fork.ι c) ⋯)

Every kernel of f induces a kernel of f ≫ g if g is mono.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Kernels

Cited by

3 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Mono