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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.isPullback_SpecMap_of_isPushout

∀ {A B C P : CommRingCat} (f : A ⟶ B) (g : A ⟶ C) (inl : B ⟶ P) (inr : C ⟶ P),
  CategoryTheory.IsPushout f g inl inr →
    CategoryTheory.IsPullback (AlgebraicGeometry.Spec.map inl) (AlgebraicGeometry.Spec.map inr)
      (AlgebraicGeometry.Spec.map f) (AlgebraicGeometry.Spec.map g)
Defined in
Mathlib.AlgebraicGeometry.Pullbacks
Cited by
2 results in Mathlib
Foundations
Depth 142 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.IsIntegralHom.iff_universallyClosed_and_isAffineHom · cited by 2IsIntegralHom.iff_univers…AlgebraicGeometry.isPullback_SpecMap_pushout · cited by 1AlgebraicGeometry.isPullb…Quiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatAlgebraicGeometry.Spec · cited by 626AlgebraicGeometry.SpecAlgebraicGeometry.Spec.map · cited by 332Spec.mapCategoryTheory.IsPullback · cited by 320CategoryTheory.IsPullbackCategoryTheory.IsPushout · cited by 219CategoryTheory.IsPushoutCategoryTheory.IsPullback.flip · cited by 61IsPullback.flipAlgebraicGeometry.Scheme.Spec · cited by 57Scheme.SpecCategoryTheory.IsPullback.map · cited by 20IsPullback.mapCategoryTheory.IsPushout.op · cited by 7IsPushout.opAlgebraicGeometry.isPullback_…CITED BYCITES

Cites11

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Cited by2

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