Theorems · Definition · commutative algebra
Shrink.algEquiv
(R : Type u_1) →
(α : Type u_2) →
[inst : Small.{v, u_2} α] →
[inst_1 : CommSemiring R] → [inst_2 : Semiring α] → [inst_3 : Algebra R α] → Shrink.{v, u_2} α ≃ₐ[R] αShrinking α to a smaller universe preserves algebra structure.
- Defined in
- Mathlib.Algebra.Algebra.Shrink
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Equiv.symmproof · cited by 3,681
- AlgEquivstatement · cited by 1,681
- Smallstatement and proof · cited by 369
- Shrinkstatement · cited by 132
- equivShrinkproof · cited by 118
- Equiv.algEquivproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Algebra.FormallyUnramified.iff_comp_injective_of_smallproof · cited by 4
- Algebra.ZariskisMainProperty.of_finiteType_of_weaklyQuasiFiniteAtproof · cited by 3
- Shrink.algEquiv_symm_applystatement and proof · cited by 1
- Shrink.algEquiv_applystatement and proof · cited by 0