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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.isPullback_SpecMap_pushout

∀ {A B C : CommRingCat} (f : A ⟶ B) (g : A ⟶ C),
  CategoryTheory.IsPullback (AlgebraicGeometry.Spec.map (CategoryTheory.Limits.pushout.inl f g))
    (AlgebraicGeometry.Spec.map (CategoryTheory.Limits.pushout.inr f g)) (AlgebraicGeometry.Spec.map f)
    (AlgebraicGeometry.Spec.map g)
Defined in
Mathlib.AlgebraicGeometry.Pullbacks
Cited by
1 results in Mathlib
Foundations
Depth 143 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.Scheme.Pullback.Triplet.isPullback_SpecMap_tensor · cited by 1Triplet.isPullback_SpecMa…Quiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatCategoryTheory.Limits.WalkingPair · cited by 1319Limits.WalkingPairAlgebraicGeometry.Spec · cited by 626AlgebraicGeometry.SpecAlgebraicGeometry.Spec.map · cited by 332Spec.mapCategoryTheory.IsPullback · cited by 320CategoryTheory.IsPullbackCategoryTheory.Limits.WalkingSpan · cited by 300Limits.WalkingSpanCategoryTheory.Limits.span · cited by 294Limits.spanCategoryTheory.Limits.pushout · cited by 284Limits.pushoutCategoryTheory.Limits.pushout.inr · cited by 193pushout.inrCategoryTheory.Limits.pushout.inl · cited by 192pushout.inlCategoryTheory.IsPushout.of_hasPushout · cited by 20IsPushout.of_hasPushoutAlgebraicGeometry.isPullback_SpecMap_of_isPushout · cited by 2AlgebraicGeometry.isPullb…AlgebraicGeometry.isPullback_…CITED BYCITES

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