Theorems · Definition · category theory

CategoryTheory.Limits.Pi.reindex

{β : Type w} →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      {γ : Type w'} →
        (ε : β ≃ γ) →
          (f : γ → C) →
            [inst_1 : CategoryTheory.Limits.HasProduct f] →
              [inst_2 : CategoryTheory.Limits.HasProduct (f ∘ ⇑ε)] → ∏ᶜ f ∘ ⇑ε ≅ ∏ᶜ f

Reindex a categorical product via an equivalence of the index types.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Products

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasProductCategoryTheory.Limits.HasProduct