Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.pretopology
(P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme) → [P.IsStableUnderBaseChange] → [P.IsMultiplicative] → CategoryTheory.Pretopology AlgebraicGeometry.Scheme
The pretopology on the category of schemes defined by covering families where the components
satisfy P.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AlgebraicGeometry.Scheme.precoverageproof · cited by 336
- CategoryTheory.MorphismProperty.IsMultiplicativestatement and proof · cited by 332
- CategoryTheory.MorphismProperty.IsStableUnderBaseChangestatement and proof · cited by 131
- CategoryTheory.Pretopologystatement · cited by 32
- CategoryTheory.Precoverage.toPretopologyproof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.zariskiPretopologyproof · cited by 1
- AlgebraicGeometry.Scheme.Cover.mem_pretopologystatement · cited by 1
- AlgebraicGeometry.Scheme.mem_pretopology_iffstatement · cited by 1
- AlgebraicGeometry.Scheme.pretopology.congr_simpstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.exists_cover_of_mem_pretopologystatement · cited by 0
- AlgebraicGeometry.Scheme.pretopology_eq_infstatement · cited by 0
- AlgebraicGeometry.Scheme.pretopology_monotonestatement · cited by 0
- AlgebraicGeometry.Scheme.etalePretopologyproof · cited by 0