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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.appLE_map

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) {U : Y.Opens} {V V' : X.Opens}
  (e : V ≤ (TopologicalSpace.Opens.map f.base).obj U) (i : Opposite.op V ⟶ Opposite.op V'),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.appLE f U V e) (X.presheaf.map i) =
    AlgebraicGeometry.Scheme.Hom.appLE f U V' ⋯
Defined in
Mathlib.AlgebraicGeometry.Scheme
Cited by
27 results in Mathlib
Foundations
Depth 102 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.SpecMap_stalkMap_fromSpecStalk · cited by 8Scheme.SpecMap_stalkMap_f…AlgebraicGeometry.IsAffineOpen.SpecMap_appLE_fromSpec · cited by 8IsAffineOpen.SpecMap_appL…AlgebraicGeometry.Scheme.Opens.toSpecΓ_naturality · cited by 4Opens.toSpecΓ_naturalityAlgebraicGeometry.Scheme.Hom.appLE_map_assoc · cited by 4Hom.appLE_map_assocAlgebraicGeometry.HasRingHomProperty.iff_exists_appLE_locally · cited by 3HasRingHomProperty.iff_ex…AlgebraicGeometry.Proj.awayι_comp_map · cited by 3Proj.awayι_comp_mapAlgebraicGeometry.morphismRestrict_appLE · cited by 3AlgebraicGeometry.morphis…AlgebraicGeometry.exists_appTop_π_eq_of_isLimit · cited by 2AlgebraicGeometry.exists_…AlgebraicGeometry.exists_app_map_eq_zero_of_isLimit · cited by 2AlgebraicGeometry.exists_…AlgebraicGeometry.HasRingHomProperty.of_source_openCover · cited by 2HasRingHomProperty.of_sou…AlgebraicGeometry.mono_pushoutSection_of_iSup_eq · cited by 2AlgebraicGeometry.mono_pu…AlgebraicGeometry.exists_smooth_of_formallySmooth_stalk · cited by 2AlgebraicGeometry.exists_…AlgebraicGeometry.Scheme.Hom.iInf_ker_openCover_map_comp_apply · cited by 2Hom.iInf_ker_openCover_ma…AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimage · cited by 2Hom.toNormalization_app_p…AlgebraicGeometry.isIso_pushoutSection_of_iSup_eq · cited by 2AlgebraicGeometry.isIso_p…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.Category.assoc · cited by 6433Category.assocTopCat.carrier · cited by 3184TopCat.carrierLE.le.trans · cited by 3151le.transAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatOpposite.unop · cited by 2231Opposite.unopTopologicalSpace.Opens · cited by 2040TopologicalSpace.OpensAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…Quiver.Hom.op · cited by 1948Hom.opHom.appLE_mapCITED BYCITES

Cites29

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Cited by27

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