Theorems · Definition · category theory

CategoryTheory.SimplicialObject.equivalenceRightToLeft

{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) →
          (X ⟶ F.augmentedCechNerve) → (CategoryTheory.SimplicialObject.Augmented.toArrow.obj X ⟶ F)

A helper function used in defining the Čech adjunction.

Defined in

Mathlib.AlgebraicTopology.CechNerve

Cited by

3 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasWidePullback