Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Cover.Hom.sigma
{P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} →
{S : AlgebraicGeometry.Scheme} →
[inst : AlgebraicGeometry.IsZariskiLocalAtSource P] →
[inst_1 : UnivLE.{v, u}] →
{𝒰 𝒱 : AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) S} →
(𝒰 ⟶ 𝒱) → (𝒰.sigma ⟶ 𝒱.sigma)A refinement of coverings induces a refinement on the single object coverings.
- Defined in
- Mathlib.AlgebraicGeometry.Cover.Sigma
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.PreZeroHypercover.I₀proof · cited by 763
- CategoryTheory.PreZeroHypercover.Xproof · cited by 649
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverproof · cited by 469
- AlgebraicGeometry.Scheme.precoveragestatement and proof · cited by 336
- CategoryTheory.Limits.Sigma.ιproof · cited by 205
- CategoryTheory.PreZeroHypercover.Hom.s₀proof · cited by 129
- CategoryTheory.PreZeroHypercover.Hom.h₀proof · cited by 93
- AlgebraicGeometry.Scheme.Coverstatement and proof · cited by 88
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Cover.sigmaFunctorproof · cited by 2
- AlgebraicGeometry.Scheme.Cover.Hom.sigma_h₀statement and proof · cited by 0
- AlgebraicGeometry.Scheme.Cover.Hom.sigma_s₀statement and proof · cited by 0
- AlgebraicGeometry.Scheme.Cover.sigmaFunctor_mapstatement · cited by 0