Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsZariskiLocalAtSource.comp
∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} [AlgebraicGeometry.IsZariskiLocalAtSource P]
{X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y} {UX : AlgebraicGeometry.Scheme},
P f → ∀ (i : UX ⟶ X) [AlgebraicGeometry.IsOpenImmersion i], P (CategoryTheory.CategoryStruct.comp i f)- Cited by
- 10 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.
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
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- AlgebraicGeometry.IsOpenImmersionstatement and proof · cited by 476
- AlgebraicGeometry.Scheme.affineCoverproof · cited by 61
- AlgebraicGeometry.IsZariskiLocalAtSourcestatement and proof · cited by 37
- AlgebraicGeometry.Scheme.Cover.addproof · cited by 4
- CategoryTheory.MorphismProperty.iff_of_zeroHypercover_sourceproof · cited by 3
Cited by10
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsZariskiLocalAtSource.iff_of_openCoverproof · cited by 13
- AlgebraicGeometry.IsZariskiLocalAtSource.of_isOpenImmersionproof · cited by 5
- AlgebraicGeometry.IsZariskiLocalAtSource.iff_of_iSup_eq_topproof · cited by 3
- AlgebraicGeometry.IsZariskiLocalAtSource.resLEproof · cited by 2
- AlgebraicGeometry.isSheaf_type_propQCTopology_iffproof · cited by 1
- AlgebraicGeometry.HasRingHomProperty.descendsAlongproof · cited by 1
- AlgebraicGeometry.universally_isZariskiLocalAtSourceproof · cited by 0
- AlgebraicGeometry.IsZariskiLocalAtSource.isZariskiLocalAtTargetproof · cited by 0
- AlgebraicGeometry.isOpenMap_of_generalizingMapproof · cited by 0