论文标题
代数模式的信封
Envelopes for Algebraic Patterns
论文作者
论文摘要
我们将Lurie的构造构建为$ \ infty $ -OPERAD的对称单层封面设置为代数模式。当切成终端对象的信封时，这个信封将变得完全忠实，我们表征了它的基本形象。使用此情况，我们证明了一个比较结果，该结果使我们能够比较$ \ infty $ - operads在各种代数模式上进行比较。特别是，我们表明，$ g $ - $ \ infty $ -operads nardin-shah等同于$（2，1）$ - 类别$ \ mathrm {spanrm {span}（\ mathbb {f} _g）$ g $ g $ - $ g $ -sets的“纤维图案”。当$ g $很琐碎时，这意味着可以在$ \ mathrm {span}（\ Mathbb {f}）$而不是$ \ mathbb {f} _*$上等效地定义lurie的$ \ infty $ -operads。
We generalize Lurie's construction of the symmetric monoidal envelope of an $\infty$-operad to the setting of algebraic patterns. This envelope becomes fully faithful when sliced over the envelope of the terminal object, and we characterize its essential image. Using this, we prove a comparison result that allows us to compare analogues of $\infty$-operads over various algebraic patterns. In particular, we show that the $G$-$\infty$-operads of Nardin-Shah are equivalent to "fibrous patterns" over the $(2, 1)$-category $\mathrm{Span}(\mathbb{F}_G)$ of spans of finite $G$-sets. When $G$ is trivial this means that Lurie's $\infty$-operads can equivalently be defined over $\mathrm{Span}(\mathbb{F})$ instead of $\mathbb{F}_*$.
