Theorems · Definition · category theory

CategoryTheory.Limits.piEquivalenceFunctorDiscreteCompColim

(α : Type w₂) →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      [inst_1 : CategoryTheory.Limits.HasCoproductsOfShape α C] →
        (CategoryTheory.piEquivalenceFunctorDiscrete α C).functor.comp CategoryTheory.Limits.colim ≅
          CategoryTheory.Limits.Sigma.functor α

Up to pre-composing with an equivalence of categories, Sigma.functor is isomorphic to colim.

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.HasCoproductsOfShape