Theorems · Definition · category theory

CategoryTheory.Limits.kernelBiproductToSubtypeIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {K : Type} →
        [inst_2 : Finite K] →
          [inst_3 : CategoryTheory.Limits.HasFiniteBiproducts C] →
            (f : K → C) →
              (p : K → Prop) →
                CategoryTheory.Limits.kernel (CategoryTheory.Limits.biproduct.toSubtype f p) ≅ ⨁ Subtype.restrict pᶜ f

The kernel of biproduct.toSubtype f p is ⨁ Subtype.restrict pᶜ f.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Biproducts

Cited by

2 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsFiniteCategoryTheory.Limits.HasFiniteBiproducts