Theorems · Definition · category theory

CategoryTheory.Limits.piObjIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {D : Type u₁} →
      [inst_1 : CategoryTheory.Category.{v₁, u₁} D] →
        {α : Type w} →
          [inst_2 : CategoryTheory.Limits.HasLimitsOfShape (CategoryTheory.Discrete α) C] →
            (f : α → CategoryTheory.Functor D C) → (d : D) → (∏ᶜ f).obj d ≅ ∏ᶜ fun s => (f s).obj d

Evaluating a product of functors amounts to taking the product of the evaluations.

Defined in

Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Products

Cited by

7 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasLimitsOfShape