Theorems · Theorem · commutative algebra

CharacterModule.dual_rTensor_conj_homEquiv

∀ {R : Type uR} [inst : CommRing R] {A : Type uA} [inst_1 : AddCommGroup A] (A' : Type u_1) [inst_2 : AddCommGroup A']
  {B : Type uB} [inst_3 : AddCommGroup B] [inst_4 : Module R A] [inst_5 : Module R A'] [inst_6 : Module R B]
  (f : A →ₗ[R] A'),
  ↑CharacterModule.homEquiv.symm ∘ₗ CharacterModule.dual (LinearMap.rTensor B f) ∘ₗ ↑CharacterModule.homEquiv =
    LinearMap.lcomp R (CharacterModule B) f

Defined in: Mathlib.Algebra.Module.CharacterModule
Cited by: 0 results in Mathlib
Foundations: Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup AddCommGroup AddCommGroup Module Module Module

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Modulestatement and proof · cited by 20,661
RingHom.idstatement and proof · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
LinearMapstatement and proof · cited by 10,215
TensorProductstatement · cited by 2,545
LinearMap.compstatement · cited by 1,642
LinearEquiv.symmstatement · cited by 1,461
LinearEquiv.toLinearMapstatement · cited by 1,171
LinearMap.rTensorstatement · cited by 266
CharacterModulestatement · cited by 26
LinearMap.lcompstatement · cited by 16

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