Theorems · Theorem · ring theory
HopfAlgebra.Quotient.antipode_mk
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : HopfAlgebraStruct R A] (I : Ideal A)
[inst_3 : I.IsTwoSided] [inst_4 : Ideal.IsHopfIdeal R I] (a : A),
(HopfAlgebraStruct.antipode R) ((Ideal.Quotient.mk I) a) = (Ideal.Quotient.mk I) ((HopfAlgebraStruct.antipode R) a)- Defined in
- Mathlib.RingTheory.HopfAlgebra.Quotient
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- Ideal.Quotient.mkstatement · cited by 610
- Ideal.IsTwoSidedstatement and proof · cited by 179
- HopfAlgebraStruct.antipodestatement · cited by 38
- HopfAlgebraStructstatement and proof · cited by 6
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