Theorems · Definition · category theory
CommAlgCat.algEquivOfIso
{R : Type u} → [inst : CommRing R] → {A B : CommAlgCat R} → (A ≅ B) → ↑A ≃ₐ[R] ↑BBuild an AlgEquiv from an isomorphism in the category CommAlgCat R.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
- Assumes
- CommRing
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.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- CategoryTheory.Isostatement and proof · cited by 3,963
- AlgHomproof · cited by 3,236
- AlgEquivstatement · cited by 1,681
- CommAlgCatstatement and proof · cited by 96
- CommAlgCat.carrierstatement and proof · cited by 77
- CommAlgCat.Hom.homproof · cited by 39
Cited by4
Results whose statement or proof uses this declaration.
- CommAlgCat.isoEquivAlgEquivproof · cited by 2
- CommAlgCat.isoEquivAlgEquiv_applystatement · cited by 0
- CommAlgCat.algEquivOfIso_applystatement and proof · cited by 0
- CommAlgCat.algEquivOfIso_symm_applystatement and proof · cited by 0