Theorems · Definition · ring theory

Bialgebra.TensorProduct.map

{R : Type u_1} →
  {S : Type u_2} →
    {A : Type u_3} →
      {B : Type u_4} →
        {C : Type u_5} →
          {D : Type u_6} →
            [inst : CommSemiring R] →
              [inst_1 : CommSemiring S] →
                [inst_2 : Semiring A] →
                  [inst_3 : Semiring B] →
                    [inst_4 : Bialgebra S A] →
                      [inst_5 : Bialgebra R B] →
                        [inst_6 : Algebra R A] →
                          [inst_7 : Algebra R S] →
                            [inst_8 : IsScalarTower R S A] →
                              [inst_9 : Semiring C] →
                                [inst_10 : Semiring D] →
                                  [inst_11 : Bialgebra S C] →
                                    [inst_12 : Bialgebra R D] →
                                      [inst_13 : Algebra R C] →
                                        [inst_14 : IsScalarTower R S C] →
                                          (A →ₐc[S] C) → (B →ₐc[R] D) → TensorProduct R A B →ₐc[S] TensorProduct R C D

The tensor product of two bialgebra morphisms as a bialgebra morphism.

Defined in

Mathlib.RingTheory.Bialgebra.TensorProduct

Cited by

8 results in Mathlib

Foundations

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

Assumes

CommSemiringCommSemiringSemiringSemiringBialgebraBialgebraAlgebraAlgebraIsScalarTowerSemiringSemiringBialgebraBialgebraAlgebraIsScalarTower