Theorems · Theorem · ring theory

BialgHom.convMul_def

∀ {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 A] [inst_4 : Bialgebra R C] [inst_5 : Coalgebra.IsCocomm R C] (f g : WithConv (C →ₐc[R] A)),
  f * g =
    WithConv.toConv
      ((Bialgebra.mulBialgHom R A).comp
        ((Bialgebra.TensorProduct.map f.ofConv g.ofConv).comp (Bialgebra.comulBialgHom R C)))

Defined in

Mathlib.RingTheory.Bialgebra.Convolution

Cited by

0 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringSemiringBialgebraBialgebraCoalgebra.IsCocomm