Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isIso_SpecMap_iff
∀ {R S : CommRingCat} {f : R ⟶ S},
CategoryTheory.IsIso (AlgebraicGeometry.Spec.map f) ↔ Function.Bijective ⇑(CommRingCat.Hom.hom f)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- RingHomstatement · cited by 10,189
- AlgebraicGeometry.Schemestatement · cited by 2,540
- CommRingCatstatement and proof · cited by 2,333
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CommRingCat.carrierstatement · cited by 1,096
- Function.Bijectivestatement · cited by 863
- AlgebraicGeometry.Specstatement · cited by 626
- CommRingCat.Hom.homstatement · cited by 432
- AlgebraicGeometry.Spec.mapstatement and proof · cited by 332
- AlgebraicGeometry.Scheme.Hom.appTopproof · cited by 109
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