Theorems · Definition · category theory

CategoryTheory.Limits.kernelSubobjectIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y : C} →
      [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
        (f : X ⟶ Y) →
          [inst_2 : CategoryTheory.Limits.HasKernel f] →
            CategoryTheory.Subobject.underlying.obj (CategoryTheory.Limits.kernelSubobject f) ≅
              CategoryTheory.Limits.kernel f

The underlying object of kernelSubobject f is (up to isomorphism!) the same as the chosen object kernel f.

Defined in

Mathlib.CategoryTheory.Subobject.Limits

Cited by

20 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasKernel