Theorems · Theorem · category theory

TopCat.Presheaf.SheafConditionEqualizerProducts.piOpens.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.piOpens F U},
  (∀ (j : CategoryTheory.Discrete ι),
      CategoryTheory.CategoryStruct.comp f
          (CategoryTheory.Limits.limit.π (CategoryTheory.Discrete.functor fun i => F.obj (Opposite.op (U i))) j) =
        CategoryTheory.CategoryStruct.comp f'
          (CategoryTheory.Limits.limit.π (CategoryTheory.Discrete.functor fun i => F.obj (Opposite.op (U i))) j)) →
    f = f'

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

Defined in

Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts

Cited by

1 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasProducts