We show that there is no distributive law of the free lattice monad over the powerset monad. The proof presented here also works for other classes of lattices such as (bounded) distributive/modular lattices and also for some variants of the powerset monad such as the (nonempty) finite powerset monad.

中文翻译：

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格不会在幂集上分配

我们证明了自由格数单子在幂集单子上没有分布律。此处提供的证明还适用于其他类别的晶格，例如（有界）分布/模数晶格，也适用于幂集单子的某些变体，例如（非空）有限幂集单子。