Theorems · Theorem · ring theory

Coalgebra.Repr.tmul_left

∀ {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}
  (ℛa : Coalgebra.Repr R a ι) (ℛb : Coalgebra.Repr R b κ) (i : ι × κ),
  (ℛa.tmul ℛb).left i = ℛa.left i.1 ⊗ₜ[R] ℛb.left i.2

Defined in

Mathlib.RingTheory.Bialgebra.TensorProduct

Cited by

1 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringBialgebraSemiringBialgebra