Mathlib Map

Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.PartialMap.restrict

{X Y : AlgebraicGeometry.Scheme} → (f : X.PartialMap Y) → (U : X.Opens) → Dense ↑U → U ≤ f.domain → X.PartialMap Y

The restriction of a partial map to a smaller domain.

Defined in
Mathlib.AlgebraicGeometry.Birational.RationalMap
Cited by
31 results in Mathlib
Foundations
Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

AlgebraicGeometry.Scheme.PartialMap.equiv · cited by 18PartialMap.equivAlgebraicGeometry.Scheme.PartialMap.restrict_hom · cited by 3PartialMap.restrict_homAlgebraicGeometry.Scheme.PartialMap.comp_equiv_of_equiv_left · cited by 3PartialMap.comp_equiv_of_…AlgebraicGeometry.Scheme.PartialMap.restrict_toRationalMap · cited by 2PartialMap.restrict_toRat…AlgebraicGeometry.Scheme.PartialMap.equiv.trans · cited by 2equiv.transAlgebraicGeometry.Scheme.PartialMap.comp_equiv_of_equiv_right · cited by 2PartialMap.comp_equiv_of_…AlgebraicGeometry.Scheme.PartialMap.equiv_iff_of_isSeparated_of_le · cited by 2PartialMap.equiv_iff_of_i…AlgebraicGeometry.Scheme.PartialMap.equiv_of_restrict_eq · cited by 2PartialMap.equiv_of_restr…AlgebraicGeometry.Scheme.PartialMap.fromSpecStalkOfMem_restrict · cited by 2PartialMap.fromSpecStalkO…AlgebraicGeometry.Scheme.PartialMap.isDominant_hom_iff_of_equiv · cited by 2PartialMap.isDominant_hom…AlgebraicGeometry.Scheme.PartialMap.isOver_iff_eq_restrict · cited by 1PartialMap.isOver_iff_eq_…AlgebraicGeometry.Scheme.PartialMap.restrict_equiv · cited by 1PartialMap.restrict_equivAlgebraicGeometry.Scheme.PartialMap.toPartialMap_toRationalMap_restrict · cited by 1PartialMap.toPartialMap_t…AlgebraicGeometry.Scheme.PartialMap.equiv.symm · cited by 1equiv.symmAlgebraicGeometry.Scheme.PartialMap.comp_restrict_left · cited by 1PartialMap.comp_restrict_…CategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compSetLike.coe · cited by 8199SetLike.coeTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…AlgebraicGeometry.Scheme.Opens · cited by 1149Scheme.OpensDense · cited by 359DenseAlgebraicGeometry.Scheme.homOfLE · cited by 103Scheme.homOfLEAlgebraicGeometry.Scheme.PartialMap · cited by 76Scheme.PartialMapAlgebraicGeometry.Scheme.PartialMap.domain · cited by 60PartialMap.domainAlgebraicGeometry.Scheme.PartialMap.hom · cited by 49PartialMap.homPartialMap.restrictCITED BYCITES

Cites15

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Cited by32

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