map_bot — Mathlib

English

For any nonunital algebra hom f: A →ₙₐ[R] B, the comap of the top subalgebra ⊤ of B along f equals ⊤ in A.

Русский

Предобраз верхней подпалгебры ⊤ в B по f равен ⊤ в A.

LaTeX

$$$(\top : NonUnitalSubalgebra R B).comap f = \top$$$

Lean4

@[simp]
theorem map_bot [IsScalarTower R B B] [SMulCommClass R B B] (f : A →ₙₐ[R] B) :
    (⊥ : NonUnitalSubalgebra R A).map f = ⊥ :=
  SetLike.coe_injective <| by simp [NonUnitalAlgebra.coe_bot, NonUnitalSubalgebra.coe_map]

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