Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Cover.functorOfLocallyDirected
{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] →
[𝒰.LocallyDirected] → CategoryTheory.Functor 𝒰.I₀ AlgebraicGeometry.SchemeThe canonical diagram induced by a locally directed cover.
- Defined in
- Mathlib.AlgebraicGeometry.Cover.Directed
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 110 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.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functorstatement · cited by 16,252
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.PreZeroHypercover.I₀statement and proof · cited by 763
- CategoryTheory.PreZeroHypercover.Xproof · cited by 649
- 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
- AlgebraicGeometry.Scheme.Cover.LocallyDirectedstatement and proof · cited by 63
- AlgebraicGeometry.Scheme.Cover.transproof · cited by 43
Cited by23
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.natTransstatement · cited by 8
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.ι_toBasestatement · cited by 4
- AlgebraicGeometry.Scheme.Cover.functorOfLocallyDirectedHomBasestatement · cited by 4
- AlgebraicGeometry.Scheme.Cover.coconeOfLocallyDirectedstatement · cited by 2
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.mk.injstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.mk.noConfusionstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.equifiberedstatement · cited by 1
- AlgebraicGeometry.Scheme.OpenCover.isColimitCoconeOfLocallyDirectedstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.isPullback_natTrans_ι_toBasestatement · cited by 0
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.noConfusionproof · cited by 0
- AlgebraicGeometry.Scheme.Cover.RelativeGluingData.noConfusionTypeproof · cited by 0