The present article exploits the fact that permutads (aka shuffle algebras) are algebras over a terminal operad in a certain operadic category Per. In the first, classical part we formulate and prove a claim envisaged by Loday and Ronco that the cellular chains of the permutohedra form the minimal model of the terminal permutad which is moreover, in the sense we define, self-dual and Koszul. In the second part we study Koszulity of Per-operads. Among other things we prove that the terminal Per-operad is Koszul self-dual. We then describe strongly homotopy permutads as algebras of its minimal model. Our paper shall advertise analogous future results valid in general operadic categories, and the prominent rôle of operadic (op)fibrations in the related theory.

本文利用了这样的事实，即置换（aka shuffle代数）是在某个操作数类别Per中操作的终端上的代数。在第一部分的经典部分中，我们提出并证明了Loday和Ronco所设想的一种说法，即变体动物的细胞链形成了终生变体的最小模型，而且在我们定义的意义上，它是自对偶的和Koszul。在第二部分中，我们研究每个操作符的Koszulity。除其他外，我们证明终端Per -operad是Koszul自对偶。然后，我们将强同伦置换元描述为其最小模型的代数。我们的论文将宣传在一般操作分类中有效的类似未来结果，以及相关理论中突出的操作（op）纤维作用。