Theorems · Definition · commutative algebra

Module.Invertible.rTensorInv

{R : Type u} →
  {M : Type v} →
    {N : Type u_1} →
      (P : Type u_2) →
        (Q : Type u_3) →
          [inst : CommSemiring R] →
            [inst_1 : AddCommMonoid M] →
              [inst_2 : AddCommMonoid N] →
                [inst_3 : AddCommMonoid P] →
                  [inst_4 : AddCommMonoid Q] →
                    [inst_5 : Module R M] →
                      [inst_6 : Module R N] →
                        [inst_7 : Module R P] →
                          [inst_8 : Module R Q] →
                            (TensorProduct R M N ≃ₗ[R] R) →
                              (TensorProduct R P M →ₗ[R] TensorProduct R Q M) →ₗ[R] P →ₗ[R] Q

If M is invertible, rTensorHom M admits an inverse.

Defined in

Mathlib.RingTheory.PicardGroup

Cited by

2 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleModule