Theorems · Definition · category theory

CategoryTheory.Limits.kernelIsKernel

{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] →
            CategoryTheory.Limits.IsLimit (CategoryTheory.Limits.Fork.ofι (CategoryTheory.Limits.kernel.ι f) ⋯)

The kernel built from kernel.ι f is limiting.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Kernels

Cited by

24 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasKernel