Theorems · Theorem · algebraic geometry

TopCat.Presheaf.EtaleSpace.homeomorph.congr_simp

∀ {X : TopCat} {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {CC : C → Type v} {FC : C → C → Type w}
  [inst_1 : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)] [inst_2 : CategoryTheory.ConcreteCategory C FC]
  [inst_3 : CategoryTheory.Limits.HasColimits C] {F : TopCat.Presheaf C X}
  [inst_4 : CategoryTheory.Limits.PreservesFilteredColimits (CategoryTheory.forget C)] (U : TopologicalSpace.Opens ↑X)
  (hF_bij : ∀ (x : ↑X) (hx : x ∈ U), Function.Bijective ⇑(CategoryTheory.ConcreteCategory.hom (F.germ U x hx))) (x : ↑X)
  (hx : x ∈ U),
  TopCat.Presheaf.EtaleSpace.homeomorph U hF_bij x hx = TopCat.Presheaf.EtaleSpace.homeomorph U hF_bij x hx

Defined in

Mathlib.Topology.Sheaves.EtaleSpace

Cited by

0 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.Limits.HasColimitsCategoryTheory.Limits.PreservesFilteredColimits