Theorems · Definition · commutative algebra
RingEquiv.toCommRingCatIso
{R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → R ≃+* S → (CommRingCat.of R ≅ CommRingCat.of S)Ring equivalences are isomorphisms in category of commutative rings
- Defined in
- Mathlib.Algebra.Category.Ring.Basic
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- CategoryTheory.Isostatement · cited by 3,963
- CommRingCatstatement · cited by 2,333
- RingEquivstatement and proof · cited by 1,147
- RingHomClass.toRingHomproof · cited by 746
- RingEquiv.symmproof · cited by 567
- CommRingCat.ofHomproof · cited by 259
Cited by29
Results whose statement or proof uses this declaration.
- RingHom.toMorphismProperty_respectsIso_iffproof · cited by 11
- AlgebraicGeometry.stalkClosedPointIsoproof · cited by 9
- AlgebraicGeometry.Spec.stalkIsoproof · cited by 8
- AlgebraicGeometry.Scheme.Spec.residueFieldIsoproof · cited by 7
- AlgebraicGeometry.AffineSpace.SpecIsoproof · cited by 7
- AlgebraicGeometry.AffineSpace.SpecIso_inv_overproof · cited by 4
- AlgebraicGeometry.localRingHom_comp_stalkIsoproof · cited by 3
- RingEquiv.toCommRingCatIso_homstatement and proof · cited by 3
- AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ_ΓToStalkstatement and proof · cited by 2
- AlgebraicGeometry.ProjectiveSpectrum.Proj.specStalkEquivproof · cited by 2
- AlgebraicGeometry.Proj.stalkIsoproof · cited by 2
- CommRingCat.coyonedaUniqueproof · cited by 2