evalRingHom — Mathlib

English

There is a canonical monoid hom from ContMDiffMap to functions given by evaluation: f ↦ f, i.e., the coercion to function is a monoid hom compatible with composition and ring structure.

Русский

Существует канонический моноид-гомоморфизм из ContMDiffMap к функциям: f↦f, т.е. преобразование в функцию сохраняет моноидовую структуру.

LaTeX

$$$ContMDiffMap\; \text{coeFnMonoidHom}: C^n(I,N;I',G)\to (N\to G)$ is a monoid hom with appropriate structure.$$

Lean4

/-- `Function.eval` as a `RingHom` on the ring of `C^n` functions. -/
def evalRingHom {R : Type*} [CommRing R] [TopologicalSpace R] [ChartedSpace H' R] [ContMDiffRing I' n R] (m : N) :
    C^n⟮I, N; I', R⟯ →+* R :=
  (Pi.evalRingHom _ m : (N → R) →+* R).comp ContMDiffMap.coeFnRingHom

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