Theorems · Theorem · category theory

CategoryTheory.Limits.prod.hom_ext

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {W X Y : C}
  [inst_1 : CategoryTheory.Limits.HasBinaryProduct X Y] {f g : W ⟶ X ⨯ Y},
  CategoryTheory.CategoryStruct.comp f CategoryTheory.Limits.prod.fst =
      CategoryTheory.CategoryStruct.comp g CategoryTheory.Limits.prod.fst →
    CategoryTheory.CategoryStruct.comp f CategoryTheory.Limits.prod.snd =
        CategoryTheory.CategoryStruct.comp g CategoryTheory.Limits.prod.snd →
      f = g

Defined in

Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts

Cited by

33 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasBinaryProduct