Theorems · Theorem · category theory

CategoryTheory.Limits.coprod.hom_ext_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {W X Y : C}
  [inst_1 : CategoryTheory.Limits.HasBinaryCoproduct X Y] {f g : X ⨿ Y ⟶ W},
  f = g ↔
    CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.coprod.inl f =
        CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.coprod.inl g ∧
      CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.coprod.inr f =
        CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.coprod.inr g

Defined in

Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts

Cited by

0 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasBinaryCoproduct