Theorems · Definition · category theory

CategoryTheory.Limits.Pi.isoLimit

{α : Type w₂} →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      (X : CategoryTheory.Functor (CategoryTheory.Discrete α) C) →
        [inst_1 : CategoryTheory.Limits.HasProduct fun j => X.obj { as := j }] →
          [inst_2 : CategoryTheory.Limits.HasLimit X] → (∏ᶜ fun j => X.obj { as := j }) ≅ CategoryTheory.Limits.limit X

The isomorphism ∏ᶜ (fun j => X.obj (Discrete.mk j)) ≅ limit X.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Products

Cited by

8 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasProductCategoryTheory.Limits.HasLimit