Theorems · Definition · ring theory

Coalgebra.Repr.tmul

{R : Type u_1} →
  {A : Type u_2} →
    {B : Type u_3} →
      {ι : Type u_4} →
        {κ : Type u_5} →
          [inst : CommSemiring R] →
            [inst_1 : Semiring A] →
              [inst_2 : Bialgebra R A] →
                [inst_3 : Semiring B] →
                  [inst_4 : Bialgebra R B] →
                    {a : A} →
                      {b : B} → Coalgebra.Repr R a ι → Coalgebra.Repr R b κ → Coalgebra.Repr R (a ⊗ₜ[R] b) (ι × κ)

Representations of a and b yield a representation of a ⊗ b.

Defined in

Mathlib.RingTheory.Bialgebra.TensorProduct

Cited by

4 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringBialgebraSemiringBialgebra