Theorems · Definition · ring theory
GroupLike.toUnits
(R : Type u_1) →
{A : Type u_2} → [inst : CommSemiring R] → [inst_1 : Semiring A] → [inst_2 : HopfAlgebra R A] → GroupLike R A →* AˣTurn a group-like element a into a unit with inverse its antipode.
- Defined in
- Mathlib.RingTheory.HopfAlgebra.GroupLike
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, 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.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- CommSemiringstatement and proof · cited by 10,911
- MonoidHomstatement · cited by 3,629
- Unitsstatement · cited by 2,804
- HopfAlgebrastatement and proof · cited by 59
- HopfAlgebraStruct.antipodeproof · cited by 38
- GroupLikestatement and proof · cited by 19
- GroupLike.valproof · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- GroupLike.val_inv_toUnits_applystatement and proof · cited by 0
- IsGroupLikeElem.isUnitproof · cited by 0
- GroupLike.val_toUnits_applystatement and proof · cited by 0