论文标题
杂质和产业
Plethysms and operads
论文作者
论文摘要
我们介绍了$ \ Mathcal {t} $ - 构造，这是一种通用作业类别的内形函数，作为一种通用机制，通过这些机制，各种概念均来自更普通的替代概念。在单对象一单位作业的特殊情况下，即单人，我们恢复了Giraudo的$ t $构造。我们意识到多种散布产品是由从$ \ Mathcal {t} $ construction获得的各种作业的Bar构造的发病率的同质性基数产生的。条形结构是简单的类固醇，在终端减少的特殊情况下，$ \ mathsf {symsf {sym} $，我们恢复了Arxiv的Simplicial groupoid：1804.09462，这是普利亚（Pó）的普通成产组合模型，以pó的意义，以waldhausen $ s $ $ s $ q $ q $ q $ q $ q $ q $ q quillen $ q $ q $ q quillen。在$ \ Mathcal {t} $ - 构造的某些情况下，可以进行类似的解释。
We introduce the $\mathcal{T}$-construction, an endofunctor on the category of generalized operads as a general mechanism by which various notions of plethystic substitution arise from more ordinary notions of substitution. In the special case of one-object unary operads, i.e. monoids, we recover the $T$-construction of Giraudo. We realize several kinds of plethysm as convolution products arising from the homotopy cardinality of the incidence bialgebra of the bar construction of various operads obtained from the $\mathcal{T}$-construction. The bar constructions are simplicial groupoids, and in the special case of the terminal reduced operad $\mathsf{Sym}$, we recover the simplicial groupoid of arXiv:1804.09462, a combinatorial model for ordinary plethysm in the sense of Pólya, given in the spirit of Waldhausen $S$ and Quillen $Q$ constructions. In some of the cases of the $\mathcal{T}$-construction, an analogous interpretation is possible.
