symmEquiv — Mathlib

English

Left-composition with a fixed MulEquiv e is injective on MonoidHom M→*P.

Русский

Левая композиция с фиксированной MulEquiv e инъективна на множестве моноид-гомоморфизмов M →* P.

LaTeX

$$$$\text{Injective } (f \mapsto (e : M \to^* N).\,comp f). $$$$

Lean4

/-- `MulEquiv.symm` defines an equivalence between `α ≃* β` and `β ≃* α`. -/
@[to_additive (attr := simps!) /-- `AddEquiv.symm` defines an equivalence between `α ≃+ β` and `β ≃+ α` -/
    ]
def symmEquiv (P Q : Type*) [Mul P] [Mul Q] : (P ≃* Q) ≃ (Q ≃* P)
    where
  toFun := .symm
  invFun := .symm

Похожие утверждения