Theorems · Theorem · commutative algebra

DirectSum.decomposeTensorEquiv_apply

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  (ℳ : ι → Submodule R M) (N : Type u_5) [inst_3 : AddCommMonoid N] [inst_4 : Module R N] [inst_5 : DecidableEq ι]
  [inst_6 : DirectSum.Decomposition ℳ] {i : ι} (x : TensorProduct R (↥(ℳ i)) N),
  (DirectSum.decomposeTensorEquiv ℳ N i) x = ⟨(LinearMap.rTensor N (ℳ i).subtype) x, ⋯⟩

Defined in

Mathlib.LinearAlgebra.TensorProduct.Decomposition

Cited by

1 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModuleDecidableEqDirectSum.Decomposition