Theorems · Theorem · category theory

CategoryTheory.SimplicialObject.equivalenceRightToLeft_left

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C]
  [inst_1 :
    ∀ (n : ℕ) (f : CategoryTheory.Arrow C),
      CategoryTheory.Limits.HasWidePullback f.right (fun x => f.left) fun x => f.hom]
  (X : CategoryTheory.SimplicialObject.Augmented C) (F : CategoryTheory.Arrow C) (G : X ⟶ F.augmentedCechNerve),
  (CategoryTheory.SimplicialObject.equivalenceRightToLeft X F G).left =
    CategoryTheory.CategoryStruct.comp (G.left.app (Opposite.op { len := 0 }))
      (CategoryTheory.Limits.WidePullback.π (fun x => F.hom) 0)

Defined in

Mathlib.AlgebraicTopology.CechNerve

Cited by

0 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasWidePullback