Theorems · Theorem · linear algebra

zero_prodMap_dualTensorHom

∀ {R : Type u_2} {M : Type u_3} {N : Type u_4} {P : Type u_5} {Q : Type u_6} [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] (g : Module.Dual R N) (q : Q),
  LinearMap.prodMap 0 ((dualTensorHom R N Q) (g ⊗ₜ[R] q)) =
    (dualTensorHom R (M × N) (P × Q)) ((g ∘ₗ LinearMap.snd R M N) ⊗ₜ[R] (LinearMap.inr R P Q) q)

Defined in

Mathlib.LinearAlgebra.Contraction

Cited by

1 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleModule