Large condensation in enriched $\infty$-categories
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911029849489408 |
|---|---|
| author | Stockall, Devon |
| author_facet | Stockall, Devon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23632 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large condensation in enriched $\infty$-categories Stockall, Devon Category Theory High Energy Physics - Theory Quantum Algebra 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. |
| title | Large condensation in enriched $\infty$-categories |
| topic | Category Theory High Energy Physics - Theory Quantum Algebra |
| url | https://arxiv.org/abs/2506.23632 |