Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.grothendieckTopology
CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme → CategoryTheory.GrothendieckTopology AlgebraicGeometry.Scheme
The Grothendieck topology on the category of schemes induced by the pretopology defined by
P-covers.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.GrothendieckTopologystatement · cited by 1,415
- AlgebraicGeometry.Scheme.precoverageproof · cited by 336
- CategoryTheory.Precoverage.toGrothendieckproof · cited by 41
Cited by10
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.zariskiTopologyproof · cited by 34
- AlgebraicGeometry.Scheme.overGrothendieckTopologyproof · cited by 4
- AlgebraicGeometry.Scheme.etaleTopologyproof · cited by 2
- AlgebraicGeometry.Scheme.mem_grothendieckTopology_iffstatement · cited by 2
- AlgebraicGeometry.Scheme.Cover.mem_grothendieckTopologystatement · cited by 1
- AlgebraicGeometry.Scheme.grothendieckTopology_monotonestatement · cited by 1
- AlgebraicGeometry.Scheme.exists_cover_of_mem_grothendieckTopologystatement · cited by 1
- AlgebraicGeometry.Scheme.grothendieckTopology_eq_infstatement · cited by 0
- AlgebraicGeometry.Scheme.bot_mem_grothendieckTopologystatement and proof · cited by 0