dualCoannihilator — Mathlib

English

The dualCoannihilator of a submodule Φ ⊆ M^* is the pullback of Φ's dual annihilator along evaluation.

Русский

dualCoannihilator подмодуля Φ ⊆ M^* — это вытяжка (pullback) дуального аннигилирующего along оценивания.

LaTeX

$$def dualCoannihilator (Φ : Submodule R (Module.Dual R M)) : Submodule R M := Φ.dualAnnihilator.comap (Module.Dual.eval R M)$$

Lean4

/-- The `dualAnnihilator` of a submodule of the dual space pulled back along the evaluation map
`Module.Dual.eval`. -/
def dualCoannihilator (Φ : Submodule R (Module.Dual R M)) : Submodule R M :=
  Φ.dualAnnihilator.comap (Module.Dual.eval R M)

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