Theorems · Definition · category theory

CategoryTheory.Limits.sigmaObjIso

{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.HasColimitsOfShape (CategoryTheory.Discrete α) C] →
            (f : α → CategoryTheory.Functor D C) → (d : D) → (∐ f).obj d ≅ ∐ fun s => (f s).obj d

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

Defined in

Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Products

Cited by

4 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfShape