Theorems · Definition · category theory

TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquiv

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasProducts C] →
      {X : TopCat} →
        (F : TopCat.Presheaf C X) →
          {ι : Type v'} →
            (U : ι → TopologicalSpace.Opens ↑X) →
              CategoryTheory.Limits.Cone ((CategoryTheory.Pairwise.diagram U).op.comp F) ≌
                CategoryTheory.Limits.Cone (TopCat.Presheaf.SheafConditionEqualizerProducts.diagram F U)

Cones over diagram U ⋙ F are the same as a cones over the usual sheaf condition equalizer diagram.

Defined in

Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts

Cited by

4 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasProducts