Theorems · Definition · algebraic geometry
AlgebraicGeometry.IsLocalIso.casesOn
{X Y : AlgebraicGeometry.Scheme} →
{f : X ⟶ Y} →
{motive : AlgebraicGeometry.IsLocalIso f → Sort u_1} →
(t : AlgebraicGeometry.IsLocalIso f) →
((exists_isOpenImmersion :
∀ (x : ↥X), ∃ U, x ∈ U ∧ AlgebraicGeometry.IsOpenImmersion (CategoryTheory.CategoryStruct.comp U.ι f)) →
motive ⋯) →
motive t- Cited by
- 1 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
- AlgebraicGeometry.IsOpenImmersionstatement and proof · cited by 476
- AlgebraicGeometry.Scheme.Opens.toSchemestatement and proof · cited by 433
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isLocalIso_iffproof · cited by 1