Theorems · Theorem · algebraic geometry
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toScheme.congr_simp
∀ {X : AlgebraicGeometry.PresheafedSpace CommRingCat} (Y : AlgebraicGeometry.Scheme) (f f_1 : X ⟶ Y.toPresheafedSpace)
(e_f : f = f_1) [H : AlgebraicGeometry.PresheafedSpace.IsOpenImmersion f],
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toScheme Y f =
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toScheme Y f_1- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement and proof · cited by 2,333
- 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.PresheafedSpacestatement and proof · cited by 260
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersionstatement and proof · cited by 44
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toSchemestatement and proof · cited by 4
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