diagramNatTrans — Mathlib

English

Second form of the cocontinuity result for Over forget X with respect to J and over topology.

Русский

Вторая форма коконтинуальности Over forget X относительно J и надтопологии.

LaTeX

$$$\\forall X\\; (Over.forget X).IsCocontinuous (J.over X) J$$$

Lean4

/-- A natural transformation `P ⟶ Q` induces a natural transformation
between diagrams whose colimits define the values of `plus`. -/
@[simps]
def diagramNatTrans {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (X : C) : J.diagram P X ⟶ J.diagram Q X where
  app
    W :=
    Multiequalizer.lift _ _ (fun _ => Multiequalizer.ι _ _ ≫ η.app _)
      (fun i => by
        dsimp only
        erw [Category.assoc, Category.assoc, ← η.naturality, ← η.naturality, Multiequalizer.condition_assoc]
        rfl)

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