Theorems · Definition · category theory

CategoryTheory.Preadditive.RightFreyd.Candidate.desc

{V : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} V] →
    [inst_1 : CategoryTheory.Preadditive V] →
      [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts V] →
        {u v : CategoryTheory.Arrow V} →
          (f : u ⟶ v) →
            {w : CategoryTheory.Arrow V} →
              (g : v ⟶ w) →
                CategoryTheory.Arrow.RightHomotopy (CategoryTheory.CategoryStruct.comp f g) 0 →
                  (CategoryTheory.Preadditive.RightFreyd.Candidate.cokernel f ⟶ w)

If f : u ⟶ v and g : v ⟶ w are morphisms in Arrow V such that f ≫ g is right homotopic to 0, this is the morphism from the "candidate cokernel" of f to w defined from the right homotopy.

Defined in

Mathlib.CategoryTheory.Preadditive.FreydCategory.RightFreyd

Cited by

2 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproducts