English
Naturality of rTensor with respect to a linear map g: P → P': the equation g.rTensor(M⊗N) = assoc ∘ map(g.rTensor M) ∘ assoc^{-1}.
Русский
Естественность rTensor относительно линейного отображения g: P → P': g.rTensor(M⊗N) = assoc ∘ map(g.rTensor M) ∘ assoc^{-1}.
LaTeX
$$$g\,\mathrm{rTensor}_{R,A}(M\otimes_R N) = \text{assoc} \circ \bigl(g\,\mathrm{rTensor}_M\bigr) \circ \text{assoc}^{-1}$$$
Lean4
/-- `B`-linear equivalence between `M ⊗[A] (A ⊗[R] N)` and `M ⊗[R] N`.
In particular useful with `B = A`. -/
def cancelBaseChange : M ⊗[A] (A ⊗[R] N) ≃ₗ[B] M ⊗[R] N :=
letI g : (M ⊗[A] A) ⊗[R] N ≃ₗ[B] M ⊗[R] N := congr (AlgebraTensorModule.rid A B M) (.refl R N)
(assoc R A B M A N).symm ≪≫ₗ g