Theorems · Definition · category theory

CategoryTheory.Limits.opProductIsoCoproduct

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {α : Type u_1} →
      (Z : α → C) → [inst_1 : CategoryTheory.Limits.HasProduct Z] → Opposite.op (∏ᶜ Z) ≅ ∐ fun x => Opposite.op (Z x)

The canonical isomorphism from the opposite of the product to the coproduct in the opposite category.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products

Cited by

2 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasProduct