Theorems · Theorem · category theory

CategoryTheory.Limits.biprod.hom_ext

∀ {C : Type uC} [inst : CategoryTheory.Category.{uC', uC} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {X Y Z : C} [inst_2 : CategoryTheory.Limits.HasBinaryBiproduct X Y] (f g : Z ⟶ X ⊞ Y),
  CategoryTheory.CategoryStruct.comp f CategoryTheory.Limits.biprod.fst =
      CategoryTheory.CategoryStruct.comp g CategoryTheory.Limits.biprod.fst →
    CategoryTheory.CategoryStruct.comp f CategoryTheory.Limits.biprod.snd =
        CategoryTheory.CategoryStruct.comp g CategoryTheory.Limits.biprod.snd →
      f = g

Defined in

Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts

Cited by

34 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproduct