Theorems · Definition · category theory

CategoryTheory.CosimplicialObject.equivalenceRightToLeft

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 :
        ∀ (n : ℕ) (f : CategoryTheory.Arrow C),
          CategoryTheory.Limits.HasWidePushout f.left (fun x => f.right) fun x => f.hom] →
      (F : CategoryTheory.Arrow C) →
        (X : CategoryTheory.CosimplicialObject.Augmented C) →
          (F ⟶ CategoryTheory.CosimplicialObject.Augmented.toArrow.obj X) → (F.augmentedCechConerve ⟶ X)

A helper function used in defining the Čech conerve adjunction.

Defined in

Mathlib.AlgebraicTopology.CechNerve

Cited by

3 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasWidePushout