Theorems · Theorem · commutative algebra

Module.Invertible.rTensorEquiv_symm_apply_apply

∀ {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]
  (e : TensorProduct R M N ≃ₗ[R] R) (a : TensorProduct R P M →ₗ[R] TensorProduct R Q M) (x : P),
  ((Module.Invertible.rTensorEquiv P Q e).symm a) x =
    ((Module.Invertible.rightCancelEquiv Q e).congrRight (LinearMap.rTensor N a))
      ((TensorProduct.assoc R P M N).symm (x ⊗ₜ[R] e.symm 1))

Defined in

Mathlib.RingTheory.PicardGroup

Cited by

0 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleModule