Theorems · Definition · category theory

CategoryTheory.Precoverage.ZeroHypercover.pullbackCoverOfLeft

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : CategoryTheory.Precoverage C} →
      [J.IsStableUnderBaseChange] →
        {X : C} →
          (E : J.ZeroHypercover X) →
            {Y Z : C} →
              (f : X ⟶ Z) →
                (g : Y ⟶ Z) →
                  [inst_2 : CategoryTheory.Limits.HasPullback f g] →
                    [∀ (i : E.I₀), CategoryTheory.Limits.HasPullback (E.f i) (CategoryTheory.Limits.pullback.fst f g)] →
                      J.ZeroHypercover (CategoryTheory.Limits.pullback f g)

If {Uᵢ} covers X, this is the 0-hypercover of X ×[Z] Y given by {Uᵢ ×[Z] Y}.

Defined in

Mathlib.CategoryTheory.Sites.Hypercover.Zero

Cited by

3 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Precoverage.IsStableUnderBaseChangeCategoryTheory.Limits.HasPullbackCategoryTheory.Limits.HasPullback