Theorems · Theorem · category theory

TopCat.Presheaf.SheafConditionEqualizerProducts.piInters.hom_ext

∀ {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) {X_1 : C}
  {f f' : X_1 ⟶ TopCat.Presheaf.SheafConditionEqualizerProducts.piInters F U},
  (∀ (j : CategoryTheory.Discrete (ι × ι)),
      CategoryTheory.CategoryStruct.comp f
          (CategoryTheory.Limits.limit.π (CategoryTheory.Discrete.functor fun p => F.obj (Opposite.op (U p.1 ⊓ U p.2)))
            j) =
        CategoryTheory.CategoryStruct.comp f'
          (CategoryTheory.Limits.limit.π (CategoryTheory.Discrete.functor fun p => F.obj (Opposite.op (U p.1 ⊓ U p.2)))
            j)) →
    f = f'

Copy of limit.hom_ext, specialized to piInters for use by the ext tactic.

Defined in

Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasProducts