Theorems · Definition · category theory

CategoryTheory.CechNerveTerminalFrom.wideCospan.limitIsoPi

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasTerminal C] →
      (ι : Type w) →
        [inst_2 : CategoryTheory.Limits.HasFiniteProducts C] →
          [inst_3 : Finite ι] →
            (X : C) → CategoryTheory.Limits.limit (CategoryTheory.CechNerveTerminalFrom.wideCospan ι X) ≅ ∏ᶜ fun x => X

the isomorphism to the product induced by the limit cone wideCospan ι X

Defined in

Mathlib.AlgebraicTopology.CechNerve

Cited by

4 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasTerminalCategoryTheory.Limits.HasFiniteProductsFinite