Theorems · Theorem · category theory

CategoryTheory.Limits.biproduct.hom_ext

∀ {J : Type w} {C : Type u} [inst : CategoryTheory.Category.{v, u} C]
  [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {f : J → C} [inst_2 : CategoryTheory.Limits.HasBiproduct f]
  {Z : C} (g h : Z ⟶ ⨁ f),
  (∀ (j : J),
      CategoryTheory.CategoryStruct.comp g (CategoryTheory.Limits.biproduct.π f j) =
        CategoryTheory.CategoryStruct.comp h (CategoryTheory.Limits.biproduct.π f j)) →
    g = h

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Biproducts

Cited by

27 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBiproduct