Theorems · Definition · category theory

CategoryTheory.Limits.prod.map

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {W X Y Z : C} →
      [inst_1 : CategoryTheory.Limits.HasBinaryProduct W X] →
        [inst_2 : CategoryTheory.Limits.HasBinaryProduct Y Z] → (W ⟶ Y) → (X ⟶ Z) → (W ⨯ X ⟶ Y ⨯ Z)

If the products W ⨯ X and Y ⨯ Z exist, then every pair of morphisms f : W ⟶ Y and g : X ⟶ Z induces a morphism prod.map f g : W ⨯ X ⟶ Y ⨯ Z.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts

Cited by

105 results in Mathlib

Foundations

Depth 32 from the axioms, rests on 154 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasBinaryProductCategoryTheory.Limits.HasBinaryProduct