English
Given an R-linear isomorphism e: M2 ≃ₗ[R] M3, there is an S-linear isomorphism between the spaces of linear maps M2 →ₗ[R] M and M3 →ₗ[R] M induced by precomposition with e.
Русский
Дано R-линейное изоморфизм e: M2 ≃ₗ[R] M3, существует S-линейное изоморфизм между пространствами линейных отображений M2 →ₗ[R] M и M3 →ₗ[R] M, получаемый преддекомпозициями с e.
LaTeX
$$$ (M_2 \to_{\mathbb{R}} M) \simeq_{\mathsf{S}} (M_3 \to_{\mathbb{R}} M) $$$
Lean4
/-- If `M₂` and `M₃` are linearly isomorphic then the two spaces of linear maps from `M` into `M₂`
and `M` into `M₃` are linearly isomorphic. -/
def congrRight (f : M₂ ≃ₗ[R] M₃) : (M →ₗ[R] M₂) ≃ₗ[R] M →ₗ[R] M₃ :=
arrowCongr (LinearEquiv.refl R M) f
