Theorems · Definition · category theory

CategoryTheory.Limits.Pi.map

{β : Type w} →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      {f g : β → C} →
        [inst_1 : CategoryTheory.Limits.HasProduct f] →
          [inst_2 : CategoryTheory.Limits.HasProduct g] → ((b : β) → f b ⟶ g b) → (∏ᶜ f ⟶ ∏ᶜ g)

Construct a morphism between categorical products (indexed by the same type) from a family of morphisms between the factors.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Products

Cited by

39 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasProductCategoryTheory.Limits.HasProduct