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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.IdealSheafData.ker_fst_of_isClosedImmersion

∀ {X Y Z : AlgebraicGeometry.Scheme} (i : Z ⟶ Y) (f : X ⟶ Y) [AlgebraicGeometry.IsClosedImmersion i],
  AlgebraicGeometry.Scheme.Hom.ker (CategoryTheory.Limits.pullback.fst f i) =
    (AlgebraicGeometry.Scheme.Hom.ker i).comap f
Defined in
Mathlib.AlgebraicGeometry.IdealSheaf.Functorial
Cited by
1 results in Mathlib
Foundations
Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.IsClosedImmersion
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Around this declaration

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AlgebraicGeometry.isPullback_of_isClosedImmersion · cited by 1AlgebraicGeometry.isPullb…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.Category.comp_id · cited by 2119Category.comp_idCategoryTheory.Category.id_comp · cited by 1998Category.id_compCategoryTheory.Limits.pullback · cited by 864Limits.pullbackCategoryTheory.Limits.pullback.fst · cited by 639pullback.fstCategoryTheory.Limits.pullback.snd · cited by 637pullback.sndAlgebraicGeometry.Scheme.IdealSheafData · cited by 192Scheme.IdealSheafDataCategoryTheory.Limits.pullback.map · cited by 156pullback.mapAlgebraicGeometry.Scheme.Hom.ker · cited by 51Hom.kerAlgebraicGeometry.IsClosedImmersion · cited by 49AlgebraicGeometry.IsClose…CategoryTheory.Limits.pullback.lift_fst · cited by 40pullback.lift_fstAlgebraicGeometry.Scheme.IdealSheafData.subschemeι · cited by 36IdealSheafData.subschemeιIdealSheafData.ker_fst_of_isC…CITED BYCITES

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