congrRightRingEquiv — Mathlib

English

Let e : Y ≃+* Z be a ring equivalence. Then e induces a RingEquiv LocallyConstant(X,Y) ≃+* LocallyConstant(X,Z) by applying e pointwise.

Русский

Пусть e : Y ≃+* Z — кольцевое эквивалентность. Тогда e индуцирует RingEquiv LocallyConstant(X,Y) ≃+* LocallyConstant(X,Z), применяя e по значению элемент-wise.

LaTeX

$$$\\operatorname{congrRightRingEquiv}(e) : \\operatorname{LocallyConstant}(X,Y) \\simeq_{+*} \\operatorname{LocallyConstant}(X,Z)$$$

Lean4

/-- `LocallyConstant.congrRight` as a `RingEquiv`. -/
@[simps!]
def congrRightRingEquiv [Semiring Y] [Semiring Z] (e : Y ≃+* Z) : LocallyConstant X Y ≃+* LocallyConstant X Z
    where
  toEquiv := congrRight e
  __ := mapMonoidHom e.toMonoidHom
  __ := mapAddMonoidHom e.toAddMonoidHom

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