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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Spec.map_id

∀ (R : CommRingCat),
  AlgebraicGeometry.Spec.map (CategoryTheory.CategoryStruct.id R) =
    CategoryTheory.CategoryStruct.id (AlgebraicGeometry.Spec R)
Defined in
Mathlib.AlgebraicGeometry.Scheme
Cited by
18 results in Mathlib
Foundations
Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv · cited by 4AlgebraicGeometry.toSpecΓ…AlgebraicGeometry.pointOfClosedPoint_comp · cited by 2AlgebraicGeometry.pointOf…AlgebraicGeometry.Scheme.residueFieldCongr_fromSpecResidueField · cited by 2Scheme.residueFieldCongr_…AlgebraicGeometry.ValuativeCriterion.Existence.of_specializingMap · cited by 1Existence.of_specializing…AlgebraicGeometry.Scheme.Hom.finrank_eq_one_of_isIso · cited by 1Hom.finrank_eq_one_of_isI…AlgebraicGeometry.ext_of_apply_eq · cited by 1AlgebraicGeometry.ext_of_…AlgebraicGeometry.Scheme.Pullback.tensorCongr_SpecTensorTo · cited by 1Pullback.tensorCongr_Spec…AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ · cited by 1AlgebraicGeometry.SpecMap…AlgebraicGeometry.Scheme.stalkClosedPointTo_fromSpecStalk · cited by 0Scheme.stalkClosedPointTo…AlgebraicGeometry.Spec.map_eqToHom · cited by 0Spec.map_eqToHomAlgebraicGeometry.Spec.map_eq_id · cited by 0Spec.map_eq_idAlgebraicGeometry.isClosedImmersion_of_comp_eq_id · cited by 0AlgebraicGeometry.isClose…AlgebraicGeometry.Scheme.SpecMap_presheaf_map_eqToHom · cited by 0Scheme.SpecMap_presheaf_m…AlgebraicGeometry.Scheme.Hom.normalization.hom_ext · cited by 0normalization.hom_extAlgebraicGeometry.Spec.preimage_id · cited by 0Spec.preimage_idQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatAlgebraicGeometry.Spec · cited by 626AlgebraicGeometry.SpecAlgebraicGeometry.Spec.map · cited by 332Spec.mapAlgebraicGeometry.Scheme.Hom.ext' · cited by 5Hom.ext'AlgebraicGeometry.Spec.locallyRingedSpaceMap_id · cited by 1Spec.locallyRingedSpaceMa…Spec.map_idCITED BYCITES

Cites8

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Cited by18

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