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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.isoOpensRange_inv_comp

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [inst : AlgebraicGeometry.IsOpenImmersion f],
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.isoOpensRange f).inv f =
    (AlgebraicGeometry.Scheme.Hom.opensRange f).ι
Defined in
Mathlib.AlgebraicGeometry.Restrict
Cited by
3 results in Mathlib
Foundations
Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.IsOpenImmersion
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AlgebraicGeometry.sourceLocalClosure.iff_forall_exists · cited by 1sourceLocalClosure.iff_fo…AlgebraicGeometry.Scheme.Hom.isoOpensRange_inv_comp_assoc · cited by 0Hom.isoOpensRange_inv_com…AlgebraicGeometry.Scheme.IsLocallyDirected.fst_inv_eq_snd_inv · cited by 0IsLocallyDirected.fst_inv…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.inv · cited by 6514Iso.invAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.IsOpenImmersion · cited by 476AlgebraicGeometry.IsOpenI…AlgebraicGeometry.Scheme.Opens.toScheme · cited by 433Opens.toSchemeAlgebraicGeometry.Scheme.Opens.ι · cited by 275Opens.ιAlgebraicGeometry.Scheme.Hom.opensRange · cited by 113Hom.opensRangeAlgebraicGeometry.Scheme.Hom.isoOpensRange · cited by 17Hom.isoOpensRangeAlgebraicGeometry.IsOpenImmersion.isoOfRangeEq_inv_fac · cited by 12IsOpenImmersion.isoOfRang…Hom.isoOpensRange_inv_compCITED BYCITES

Cites10

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Cited by3

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