论文标题
外部函子和一般的经营框架
Outer functors and a general operadic framework
论文作者
论文摘要
对于$ k $ - 向量空间中的oparad $ \ nathcal {f} _ \ Mathcal {o} $，定义为$ k $ - vector {f} $ \ mathcal {f}类别，定义为$ k $ \ mathcal {o} $的类别是$ k $ - $ linear fuctors的类别，从$ k $ - $ k $ \ mathcal {o} $ to $ k $ - $ -vector-vector space。在\ Mathcal {O}（2）$中给定$μ\，满足正确的leibniz条件，完整的子类别$ \ Mathcal {f} _ \ Mathcal {o}^μ\ subset \ subset \ subset \ Mathcal {f} _ \ Mathcal {o} $及其属性及其属性介绍了。 这是由Lie Operad的情况进行的，其中$μ$被视为发电机。根据作者的先前结果，当$ k = \ mathbb {q} $，$ \ mathcal {f} _ {lie} $等同于分析函数的类别，与类别$ \ mathbf {gr} $有限生成的免费组的类别相反。主要结果表明$ \ Mathcal {f} _ {lie}^μ$ jubs与外部分析函数的类别识别，如作者对VESPA的早期工作所介绍的那样。 使用此识别，该理论适用于与Turchin和Willwacher有关的较高Hochschild同源性函数的研究。
For $\mathcal{O}$ an operad in $k$-vector spaces, the category $\mathcal{F}_\mathcal{O}$ is defined to be the category of $k$-linear functors from the PROP associated to $\mathcal{O}$ to $k$-vector spaces. Given $μ\in \mathcal{O} (2)$ that satisfies a right Leibniz condition, the full subcategory $\mathcal{F}_\mathcal{O}^μ\subset \mathcal{F}_\mathcal{O}$ is introduced here and its properties studied. This is motivated by the case of the Lie operad, where $μ$ is taken to be the generator. By previous results of the author, when $k = \mathbb{Q}$, $\mathcal{F}_{Lie}$ is equivalent to the category of analytic functors on the opposite of the category $\mathbf{gr}$ of finitely-generated free groups. The main result shows that $\mathcal{F}_{Lie}^μ$ identifies with the category of outer analytic functors, as introduced in earlier work of the author with Vespa. Using this identification, this theory has applications to the study of the higher Hochschild homology functors related to work of Turchin and Willwacher.
