Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Cover.functorOfLocallyDirectedHomBase
{P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} →
{X : AlgebraicGeometry.Scheme} →
(𝒰 : AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) X) →
[inst : CategoryTheory.Category.{v_1, u_1} 𝒰.I₀] →
[inst_1 : 𝒰.LocallyDirected] → 𝒰.functorOfLocallyDirected ⟶ (CategoryTheory.Functor.const 𝒰.I₀).obj XThe structure maps to S as a natural transformation.
- Defined in
- Mathlib.AlgebraicGeometry.Cover.Directed
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement · cited by 16,252
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Functor.conststatement · cited by 1,264
- CategoryTheory.PreZeroHypercover.I₀statement and proof · cited by 763
- CategoryTheory.PreZeroHypercover.fproof · cited by 542
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverstatement and proof · cited by 469
- AlgebraicGeometry.Scheme.precoveragestatement and proof · cited by 336
- AlgebraicGeometry.Scheme.Coverstatement and proof · cited by 88
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.toBaseproof · cited by 8
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.ι_toBaseproof · cited by 4
- AlgebraicGeometry.Scheme.Hom.ι_fromNormalizationproof · cited by 4
- AlgebraicGeometry.Scheme.Cover.coconeOfLocallyDirectedproof · cited by 2
- AlgebraicGeometry.Scheme.Cover.coconeOfLocallyDirected_ιstatement · cited by 0
- AlgebraicGeometry.Scheme.Cover.functorOfLocallyDirectedHomBase_appstatement and proof · cited by 0