Theorems · Theorem · ring theory
AlgHom.convMul_apply
∀ {R : Type u_1} {A : Type u_2} {C : Type u_4} [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : Semiring C]
[inst_3 : Bialgebra R C] [inst_4 : Algebra R A] (f g : WithConv (C →ₐ[R] A)) (c : C),
(f * g).ofConv c = (Algebra.TensorProduct.lift f.ofConv g.ofConv ⋯) (CoalgebraStruct.comul c)- Defined in
- Mathlib.RingTheory.Bialgebra.Convolution
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- mul_oneproof · cited by 3,885
- AlgHomstatement and proof · cited by 3,236
- one_mulproof · cited by 2,841
- TensorProductstatement and proof · cited by 2,545
- TensorProduct.tmulproof · cited by 1,182
- map_oneproof · cited by 861
Cited by2
Results whose statement or proof uses this declaration.
- MonoidAlgebra.convMul_algHom_single_oneproof · cited by 0
- AddMonoidAlgebra.convMul_algHom_single_oneproof · cited by 0