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 \(\textsf {Sym}\), we recover the simplicial groupoid of Cebrian (Algebraic Geom Topol 21(1):421–446, 2021), 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.

我们介绍了\({\mathcal {T}}\) - 构造，广义运算符类别的内函子，作为一种一般机制，通过这种机制，各种体积替代概念从更普通的替代概念中产生。在单对象一元操作数的特殊情况下，即幺半群，我们恢复了Giraudo 的T构造。我们实现了几种体积作为卷积乘积，这些积是由从\({\mathcal {T}}\) -构造中获得的各种运算符的条形构造的重合双代数的同伦基数引起的。条形构造是单纯类群，并且在终端简化运算符\(\textsf {Sym}\)的特殊情况下, 我们恢复了 Cebrian 的单纯群群 (Algebraic Geom Topol 21(1):421–446, 2021)，这是 Pólya 意义上的普通体积的组合模型，本着 Waldhausen S和 Quillen Q构造的精神给出。在\({\mathcal {T}}\)的某些情况下，类似的解释是可能的。