Theorems · Definition · ring theory

Bialgebra.TensorProduct.assoc

(R : Type u_1) →
  (S : Type u_2) →
    (A : Type u_3) →
      (C : Type u_5) →
        (D : Type u_6) →
          [inst : CommSemiring R] →
            [inst_1 : CommSemiring S] →
              [inst_2 : Semiring A] →
                [inst_3 : Bialgebra S A] →
                  [inst_4 : Algebra R A] →
                    [inst_5 : Algebra R S] →
                      [inst_6 : IsScalarTower R S A] →
                        [inst_7 : Semiring C] →
                          [inst_8 : Semiring D] →
                            [inst_9 : Bialgebra S C] →
                              [inst_10 : Bialgebra R D] →
                                [inst_11 : Algebra R C] →
                                  [inst_12 : IsScalarTower R S C] →
                                    TensorProduct R (TensorProduct S A C) D ≃ₐc[S]
                                      TensorProduct S A (TensorProduct R C D)

The associator for tensor products of R-bialgebras, as a bialgebra equivalence.

Defined in

Mathlib.RingTheory.Bialgebra.TensorProduct

Cited by

6 results in Mathlib

Foundations

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

Assumes

CommSemiringCommSemiringSemiringBialgebraAlgebraAlgebraIsScalarTowerSemiringSemiringBialgebraBialgebraAlgebraIsScalarTower