标题： 丰富的$\infty$-范畴中的大规模凝聚 显示英文标题

标题： Large condensation in enriched $\infty$-categories

摘要： 使用丰富化的$\infty$-范畴的语言，我们形式化并推广了融合 n-范畴的定义，以及$E_i$-代数的迭代凝聚的类似概念。前者由 Johnson-Freyd 引入，后者由 Kong、Zhang、Zhao 和 Zheng 引入。这将范畴凝聚扩展到了所有具有特定余极限的丰富化的张量$\infty$-范畴，而不仅仅是融合 n-范畴。该理论能够处理任意维度和余维度的丰富化、连续、导出、非半单和非可分的对称性。此外，我们考虑了 Gaiotto 和 Johnson-Freyd 引入的凝聚概念的一个截断变体，并证明了张量单子和$E_i$-代数的迭代凝聚提供了例子。在此过程中，我们证明了关于丰富化的$\infty$-范畴的 Day 卷积的函子性结果，以及 Eilenberg-Moore 函子两种版本的单子性结果，这些结果可能具有独立的兴趣。 显示英文摘要

摘要： Using the language of enriched $\infty$-categories, we formalize and generalize the definition of fusion n-category, and an analogue of iterative condensation of $E_i$-algebras. The former was introduced by Johnson-Freyd, and the latter by Kong, Zhang, Zhao, and Zheng. This extends categorical condensation beyond fusion n-categories to all enriched monoidal $\infty$-categories with certain colimits. The resulting theory is capable of treating symmetries of arbitrary dimension and codimension that are enriched, continuous, derived, non-semisimple and non-separable. Additionally, we consider a truncated variant of the notion of condensation introduced by Gaiotto and Johnson-Freyd, and show that iterative condensation of monoidal monads and $E_i$-algebras provide examples. In doing so, we prove results on functoriality of Day convolution for enriched $\infty$-categories, and monoidality of two versions of the Eilenberg-Moore functor, which may be of independent interest.