Theorems · Theorem · ring theory
LinearMap.algHom_comp_convOne
∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
[inst_3 : HopfAlgebra R A] [inst_4 : HopfAlgebraStruct R B] (g : A →ₐ[R] B),
g.toLinearMap ∘ₗ WithConv.ofConv 1 = WithConv.ofConv 1Post-composition by an algebra homomorphism preserves the convolution unit.
- Defined in
- Mathlib.RingTheory.HopfAlgebra.Quotient
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement and proof · cited by 3,236
- LinearMap.compstatement · cited by 1,642
- LinearMap.extproof · cited by 844
- AlgHom.toLinearMapstatement · cited by 254
- WithConvstatement · cited by 138
- CoalgebraStruct.counitproof · cited by 108
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