Theorems · Definition · category theory
commAlgCatEquivUnder
(R : CommRingCat) → CommAlgCat ↑R ≌ CategoryTheory.Under R
The category of commutative algebras over a commutative ring R is the same as commutative
rings under R.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.Functor.compproof · cited by 6,529
- CommRingCatstatement and proof · cited by 2,333
- RingEquivproof · cited by 1,147
- CommRingCat.carrierstatement and proof · cited by 1,096
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.Equivalencestatement · cited by 601
- CategoryTheory.Understatement and proof · cited by 276
- CategoryTheory.NatIso.ofComponentsproof · cited by 178
- CategoryTheory.Under.rightproof · cited by 128
- RingEquiv.toEquivproof · cited by 101
Cited by14
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.algSpecproof · cited by 13
- FGAlgCat.equivUnderproof · cited by 1
- AlgebraicGeometry.one_spec_asOver_specstatement · cited by 0
- AlgebraicGeometry.algSpec.fullyFaithfulproof · cited by 0
- commAlgCatEquivUnder_counitIsostatement and proof · cited by 0
- commAlgCatEquivUnder_functor_mapstatement and proof · cited by 0
- commAlgCatEquivUnder_functor_objstatement and proof · cited by 0
- commAlgCatEquivUnder_inverse_mapstatement and proof · cited by 0
- commAlgCatEquivUnder_inverse_obj_carrierstatement and proof · cited by 0
- commAlgCatEquivUnder_unitIsostatement and proof · cited by 0
- AlgebraicGeometry.essImage_algSpecproof · cited by 0
- AlgebraicGeometry.algSpec_map_leftstatement · cited by 0