Theorems · Theorem · algebraic geometry
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toLocallyRingedSpace.congr_simp
∀ {X : AlgebraicGeometry.PresheafedSpace CommRingCat} (Y : AlgebraicGeometry.LocallyRingedSpace)
(f f_1 : X ⟶ Y.toPresheafedSpace) (e_f : f = f_1) [H : AlgebraicGeometry.PresheafedSpace.IsOpenImmersion f],
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toLocallyRingedSpace Y f =
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toLocallyRingedSpace Y f_1- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
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
- 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.PresheafedSpacestatement and proof · cited by 260
- AlgebraicGeometry.LocallyRingedSpacestatement and proof · cited by 205
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersionstatement and proof · cited by 44
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.toLocallyRingedSpacestatement and proof · cited by 5
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