Theorems · Definition · commutative algebra

Module.Invertible.rightCancelEquiv

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

The canonical isomorphism between a module and the result of tensoring it from the right by two mutually dual invertible modules.

Defined in

Mathlib.RingTheory.PicardGroup

Cited by

4 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModule