Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.smallGrothendieckTopology
CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme →
{Q : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} →
(S : AlgebraicGeometry.Scheme) → CategoryTheory.GrothendieckTopology (Q.Over ⊤ S)If P and Q are morphism properties with P ≤ Q, this is the Grothendieck topology
induced via the forgetful functor Q.Over ⊤ S ⥤ Over S by the topology defined by P.
- Defined in
- Mathlib.AlgebraicGeometry.Sites.Small
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- CategoryTheory.Functor.idstatement · cited by 3,333
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.Discretestatement · cited by 2,447
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.GrothendieckTopologystatement · cited by 1,415
- CategoryTheory.Functor.fromPUnitstatement · cited by 769
- CategoryTheory.MorphismProperty.Overstatement · cited by 94
- CategoryTheory.Functor.restrictedTopologyproof · cited by 14
- CategoryTheory.MorphismProperty.Over.forgetproof · cited by 14
- AlgebraicGeometry.Scheme.overGrothendieckTopologyproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.smallEtaleTopologyproof · cited by 9
- AlgebraicGeometry.Scheme.smallGrothendieckTopology_eq_toGrothendieck_smallPretopologystatement · cited by 2
- AlgebraicGeometry.Scheme.mem_smallGrothendieckTopologystatement · cited by 1
- AlgebraicGeometry.Scheme.smallGrothendieckTopologyOfLEproof · cited by 0