论文标题
定向遗传物种和分解空间
Directed hereditary species and decomposition spaces
论文作者
论文摘要
我们介绍了定向的遗传物种的概念，并表明它们具有单体分解空间，comodule bialgebras和Operadic类别。这些概念涵盖了施密特（Schmitt）的遗传物种Gálvez-Kock-汤顿（Kock-kock）指示限制物种，以及Carlier的指导版本的构建单体分解空间和comodule bialgebras。 In addition to all the examples of Schmitt, Gálvez--Kock--Tonks and Carlier, the new construction covers also the Fauvet--Foissy--Manchon comodule bialgebra of finite topological spaces, the Calaque--Ebrahimi-Fard--Manchon comodule bialgebra of rooted trees, and the Faà di Bruno comodule bialgebra of linear trees.
We introduce the notion of directed hereditary species and show that they have associated monoidal decomposition spaces, comodule bialgebras, and operadic categories. The notion subsumes Schmitt's hereditary species, Gálvez--Kock--Tonks directed restrictions species, and a directed version of Carlier's construction of monoidal decomposition spaces and comodule bialgebras. In addition to all the examples of Schmitt, Gálvez--Kock--Tonks and Carlier, the new construction covers also the Fauvet--Foissy--Manchon comodule bialgebra of finite topological spaces, the Calaque--Ebrahimi-Fard--Manchon comodule bialgebra of rooted trees, and the Faà di Bruno comodule bialgebra of linear trees.
