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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.IdealSheafData.comapIso

{X Y : AlgebraicGeometry.Scheme} →
  (I : Y.IdealSheafData) → (f : X ⟶ Y) → (I.comap f).subscheme ≅ CategoryTheory.Limits.pullback f I.subschemeι

The subscheme associated to the pullback ideal sheaf is isomorphic to the fibred product.

Defined in
Mathlib.AlgebraicGeometry.IdealSheaf.Functorial
Cited by
8 results in Mathlib
Foundations
Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound
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AlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_fst · cited by 2IdealSheafData.comapIso_h…AlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_fst_assoc · cited by 2IdealSheafData.comapIso_h…AlgebraicGeometry.Scheme.IdealSheafData.comapIso_inv_subschemeι · cited by 2IdealSheafData.comapIso_i…AlgebraicGeometry.Scheme.IdealSheafData.le_map_iff_comap_le · cited by 2IdealSheafData.le_map_iff…AlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_snd · cited by 1IdealSheafData.comapIso_h…AlgebraicGeometry.Scheme.IdealSheafData.comap_comp · cited by 1IdealSheafData.comap_compAlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_snd_assoc · cited by 0IdealSheafData.comapIso_h…AlgebraicGeometry.Scheme.IdealSheafData.comapIso_inv_subschemeι_assoc · cited by 0IdealSheafData.comapIso_i…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Iso · cited by 3963CategoryTheory.IsoAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.Iso.symm · cited by 993Iso.symmCategoryTheory.Limits.pullback · cited by 864Limits.pullbackCategoryTheory.Limits.pullback.fst · cited by 639pullback.fstAlgebraicGeometry.Scheme.IdealSheafData · cited by 192Scheme.IdealSheafDataCategoryTheory.asIso · cited by 177CategoryTheory.asIsoAlgebraicGeometry.Scheme.IdealSheafData.subscheme · cited by 36IdealSheafData.subschemeAlgebraicGeometry.Scheme.IdealSheafData.subschemeι · cited by 36IdealSheafData.subschemeιAlgebraicGeometry.Scheme.IdealSheafData.comap · cited by 23IdealSheafData.comapAlgebraicGeometry.Scheme.Hom.toImage · cited by 13Hom.toImageIdealSheafData.comapIsoCITED BYCITES

Cites12

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Cited by8

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