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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.to_iso

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : AlgebraicGeometry.PresheafedSpace C} (f : X ⟶ Y)
  [H : AlgebraicGeometry.PresheafedSpace.IsOpenImmersion f] [h' : CategoryTheory.Epi f.base], CategoryTheory.IsIso f

An open immersion is an iso if the underlying continuous map is epi.

Defined in
Mathlib.Geometry.RingedSpace.OpenImmersion
Cited by
2 results in Mathlib
Foundations
Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryAlgebraicGeometry.PresheafedSpace.IsOpenImmersionCategoryTheory.Epi
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.SheafedSpace.IsOpenImmersion.to_iso · cited by 1IsOpenImmersion.to_isoAlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullback_snd_isIso_of_range_subset · cited by 0IsOpenImmersion.pullback_…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomTopologicalSpace · cited by 24529TopologicalSpaceCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorSetLike.coe · cited by 8199SetLike.coeOpposite · cited by 8081OppositeCategoryTheory.NatTrans.app · cited by 7406NatTrans.appSet.image · cited by 5609Set.imageCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homTopCat.carrier · cited by 3184TopCat.carrierIsOpen · cited by 2400IsOpenOpposite.unop · cited by 2231Opposite.unopIsOpenImmersion.to_isoCITED BYCITES

Cites39

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Cited by2

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