论文标题
关于无穷大的纠正和丰富
On rectification and enrichment of infinity properads
论文作者
论文摘要
我们开发了一种富含对称性单体无限类别的无穷大适当的理论。这些被定义为预性，满足某些类别的图形的SEGAL条件和REZK完整性条件。特别是，我们介绍了一个新的级别图形类别，这也使我们能够在富集的无限PORRAD上为代数框架提供一个框架。我们表明，可以在不改变基本理论的情况下改变图形类别。 我们还表明，无限求职者不能总是纠正，这表明第二作者的猜想和罗伯逊不太可能持有。这与无穷大营的情况形成了鲜明的对比，我们通过检查无穷大二线和无限输出的情况下进一步划分了这些情况。在这两种情况下，我们都提供了一个纠正定理，该定理说每个最新的对象都等同于严格的对象。
We develop a theory of infinity properads enriched in a general symmetric monoidal infinity category. These are defined as presheaves, satisfying a Segal condition and a Rezk completeness condition, over certain categories of graphs. In particular, we introduce a new category of level graphs which also allow us to give a framework for algebras over an enriched infinity properad. We show that one can vary the category of graphs without changing the underlying theory. We also show that infinity properads cannot always be rectified, indicating that a conjecture of the second author and Robertson is unlikely to hold. This stands in stark contrast to the situation for infinity operads, and we further demarcate these situations by examining the cases of infinity dioperads and infinity output properads. In both cases, we provide a rectification theorem that says that each up-to-homotopy object is equivalent to a strict one.
