Theorems · Definition · ring theory

CoalgHom.rTensor

{R : Type u_5} →
  (M : Type u_6) →
    {N : Type u_7} →
      {P : Type u_8} →
        [inst : CommRing R] →
          [inst_1 : AddCommGroup M] →
            [inst_2 : AddCommGroup N] →
              [inst_3 : AddCommGroup P] →
                [inst_4 : Module R M] →
                  [inst_5 : Module R N] →
                    [inst_6 : Module R P] →
                      [inst_7 : Coalgebra R M] →
                        [inst_8 : Coalgebra R N] →
                          [inst_9 : Coalgebra R P] → (N →ₗc[R] P) → TensorProduct R N M →ₗc[R] TensorProduct R P M

rTensor M f : N ⊗ M →ₗc P ⊗ M is the natural coalgebra morphism induced by f : N →ₗc P.

Defined in

Mathlib.RingTheory.Coalgebra.TensorProduct

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommRingAddCommGroupAddCommGroupAddCommGroupModuleModuleModuleCoalgebraCoalgebraCoalgebra