Theorems · Theorem · ring theory
Bialgebra.Quotient.comul_mk
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Bialgebra R A] (I : Ideal A)
[inst_3 : I.IsTwoSided] [inst_4 : (Submodule.restrictScalars R I).IsCoideal] (a : A),
CoalgebraStruct.comul ((Ideal.Quotient.mk I) a) =
(TensorProduct.map (Ideal.Quotient.mkₐ R I).toLinearMap (Ideal.Quotient.mkₐ R I).toLinearMap)
(CoalgebraStruct.comul a)- Defined in
- Mathlib.RingTheory.Bialgebra.Quotient
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
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
- TensorProductstatement · cited by 2,545
- HasQuotient.Quotientstatement · cited by 2,301
- Ideal.Quotient.mkstatement · cited by 610
- AlgHom.toLinearMapstatement · cited by 254
- TensorProduct.mapstatement · cited by 250
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