English
If e : Y ≃ₗ[R] Z is a linear equivalence, then precomposition with e induces a linear equivalence LocallyConstant(X,Y) ≃ₗ[R] LocallyConstant(X,Z).
Русский
Если e : Y ≃ₗ[R] Z является линейным эквивалентом, то предcomposition с e задаёт линейный эквивалент между LocallyConstant(X,Y) и LocallyConstant(X,Z).
LaTeX
$$$(\\operatorname{congrRight}_{\\ell} \\, e) : \\operatorname{LocallyConstant}(X,Y) \\simeq_{R} \\operatorname{LocallyConstant}(X,Z)$$$
Lean4
/-- `LocallyConstant.congrRight` as a linear equivalence. -/
@[simps!]
def congrRightₗ (R : Type*) [Semiring R] [AddCommMonoid Y] [Module R Y] [AddCommMonoid Z] [Module R Z] (e : Y ≃ₗ[R] Z) :
LocallyConstant X Y ≃ₗ[R] LocallyConstant X Z
where
toLinearMap := mapₗ R e
__ := congrRight e.toEquiv
