Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Cover.trans
{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] → {i j : 𝒰.I₀} → (i ⟶ j) → (𝒰.X i ⟶ 𝒰.X j)The transition maps of a directed cover.
- Defined in
- Mathlib.AlgebraicGeometry.Cover.Directed
- Cited by
- 43 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.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- 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.Xstatement · 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.LocallyDirected.transproof · cited by 5
Cited by60
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Cover.functorOfLocallyDirectedproof · cited by 14
- AlgebraicGeometry.Scheme.Cover.ColimitGluingData.prop_transstatement · cited by 9
- AlgebraicGeometry.Scheme.Cover.ColimitGluingData.gluedstatement and proof · cited by 7
- AlgebraicGeometry.Scheme.Cover.ColimitGluingData.relativeGluingDatastatement and proof · cited by 6
- AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMapstatement · cited by 6
- AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transstatement and proof · cited by 5
- AlgebraicGeometry.Scheme.OpenCover.glueMorphismsOfLocallyDirectedstatement and proof · cited by 4
- AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMapstatement · cited by 4
- AlgebraicGeometry.Scheme.Cover.ColimitGluingData.gluedCoconestatement and proof · cited by 4
- AlgebraicGeometry.Scheme.Cover.ColimitGluingData.pullbackGluedIsostatement and proof · cited by 4
- AlgebraicGeometry.Scheme.OpenCover.glueMorphismsOverOfLocallyDirectedstatement and proof · cited by 3
- AlgebraicGeometry.Scheme.OpenCover.map_glueMorphismsOfLocallyDirectedstatement and proof · cited by 3