mopAlgEquivOp — Mathlib

English

There is an algebra isomorphism between the MulOpposite of a subalgebra and the MulOpposite of its opposite: Sᵐᵒᵖ ≃ₐ[R] (S.op)ᵐᵒᵖ.

Русский

Существует алгебраическое изоморфизм между MulOpposite подалгебры и MulOpposite противоположности: Sᵐᵒᵖ ≃ₐ[R] (S.op)ᵐᵒᵖ.

LaTeX

$$$$S^{op} \\cong_R (S^{op})^{op}$$$$

Lean4

/-- Bijection between `MulOpposite` of a subalgebra `S` and its opposite. -/
@[simps!]
def mopAlgEquivOp (S : Subalgebra R A) : Sᵐᵒᵖ ≃ₐ[R] S.op
    where
  __ := S.toSubsemiring.mopRingEquivOp
  commutes' _ := rfl

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