Theorems · Definition · commutative algebra
AlgEquiv.toUnder
{R : CommRingCat} →
{A B : Type u} →
[inst : CommRing A] →
[inst_1 : CommRing B] →
[inst_2 : Algebra (↑R) A] → [inst_3 : Algebra (↑R) B] → (A ≃ₐ[↑R] B) → (R.mkUnder A ≅ R.mkUnder B)Make an isomorphism in Under R from an algebra isomorphism.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Algebrastatement and proof · cited by 11,388
- CategoryTheory.Isostatement · cited by 3,963
- CommRingCatstatement and proof · cited by 2,333
- AlgEquivstatement and proof · cited by 1,681
- CommRingCat.carrierstatement and proof · cited by 1,096
- AlgEquiv.symmproof · cited by 615
- CategoryTheory.Understatement · cited by 276
- AlgEquiv.toAlgHomproof · cited by 273
- CommRingCat.mkUnderstatement · cited by 24
- AlgHom.toUnderproof · cited by 10
Cited by5
Results whose statement or proof uses this declaration.
- CommRingCat.Under.tensorProductFanIsoproof · cited by 0
- AlgEquiv.toUnder_hom_right_applystatement · cited by 0
- AlgEquiv.toUnder_inv_right_applystatement · cited by 0
- AlgEquiv.toUnder_transstatement · cited by 0
- CommRingCat.Under.equalizerForkTensorProdIsoproof · cited by 0