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In this paper we characterize when a recollement of compactly generatedtriangulated categories admits a ladder of some height going either upwards ordownwards. As an application, we show that the derived category of thepreprojective algebra of Dynkin type $\mathbb{A}_n$ admits a periodic infiniteladder, where the one outer term in the recollement is the derived category ofa differential graded algebra.

Ladders of compactly generated triangulated categories and preprojective algebras