Theorems · Theorem · algebraic geometry

AlgebraicGeometry.SheafedSpace.hom_stalk_ext

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {FC : C → C → Type u_1} {CC : C → Type v}
  [inst_1 : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)] [instCC : CategoryTheory.ConcreteCategory C FC]
  [inst_2 : CategoryTheory.Limits.HasColimits C] [CategoryTheory.Limits.HasLimits C]
  [CategoryTheory.Limits.PreservesLimits (CategoryTheory.forget C)]
  [CategoryTheory.Limits.PreservesFilteredColimits (CategoryTheory.forget C)]
  [(CategoryTheory.forget C).ReflectsIsomorphisms] {X Y : AlgebraicGeometry.SheafedSpace C} (f g : X ⟶ Y)
  (h : f.hom.base = g.hom.base),
  (∀ (x : ↑↑X.toPresheafedSpace),
      AlgebraicGeometry.PresheafedSpace.Hom.stalkMap f.hom x =
        CategoryTheory.CategoryStruct.comp (Y.presheaf.stalkCongr ⋯).hom
          (AlgebraicGeometry.PresheafedSpace.Hom.stalkMap g.hom x)) →
    f = g

Defined in

Mathlib.Geometry.RingedSpace.SheafedSpace

Cited by

2 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.Limits.HasColimitsCategoryTheory.Limits.HasLimitsCategoryTheory.Limits.PreservesLimitsCategoryTheory.Limits.PreservesFilteredColimitsCategoryTheory.Functor.ReflectsIsomorphisms