Theorems · Definition · category theory

TopCat.Presheaf.SheafConditionEqualizerProducts.leftRes

{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) →
              TopCat.Presheaf.SheafConditionEqualizerProducts.piOpens F U ⟶
                TopCat.Presheaf.SheafConditionEqualizerProducts.piInters F U

The morphism Π F.obj (U i) ⟶ Π F.obj (U i) ⊓ (U j) whose components are given by the restriction maps from U i to U i ⊓ U j.

Defined in

Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts

Cited by

7 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasProducts