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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Cover.sigmaFunctor

{P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} →
  {S : AlgebraicGeometry.Scheme} →
    [AlgebraicGeometry.IsZariskiLocalAtSource P] →
      [UnivLE.{v, u}] →
        CategoryTheory.Functor (AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) S)
          (AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) S)

Collapsing a cover to a single object cover is functorial.

Defined in
Mathlib.AlgebraicGeometry.Cover.Sigma
Cited by
2 results in Mathlib
Foundations
Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.IsZariskiLocalAtSourceUnivLE
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.Scheme.Cover.sigmaFunctor_map · cited by 0Cover.sigmaFunctor_mapAlgebraicGeometry.Scheme.Cover.sigmaFunctor_obj · cited by 0Cover.sigmaFunctor_objQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…AlgebraicGeometry.Scheme.precoverage · cited by 336Scheme.precoverageAlgebraicGeometry.Scheme.Cover · cited by 88Scheme.CoverUnivLE · cited by 38UnivLEAlgebraicGeometry.IsZariskiLocalAtSource · cited by 37AlgebraicGeometry.IsZaris…AlgebraicGeometry.Scheme.Cover.sigma · cited by 12Cover.sigmaAlgebraicGeometry.Scheme.Cover.Hom.sigma · cited by 3Hom.sigmaCover.sigmaFunctorCITED BYCITES

Cites10

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Cited by2

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