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Map monoidales and duoidal $\infty$-categories
| العنوان: | Map monoidales and duoidal $\infty$-categories |
|---|---|
| المؤلفون: | Torii, Takeshi |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Category Theory, Mathematics - Algebraic Topology, 18N60 (primary), 18N70, 18M50, 55U40 (secondary) |
| الوصف: | In this paper we give an example of duoidal $\infty$-categories. We introduce map $\mathcal{O}$-monoidales in an $\mathcal{O}$-monoidal $(\infty,2)$-category for an $\infty$-operad $\mathcal{O}^{\otimes}$. We show that the endomorphism mapping $\infty$-category of a map $\mathcal{O}$-monoidale is a coCartesian $(\Delta^{\rm op},\mathcal{O})$-duoidal $\infty$-category. After that, we introduce a convolution product on the mapping $\infty$-category from an $\mathcal{O}$-comonoidale to an $\mathcal{O}$-monoidale. We show that the $\mathcal{O}$-monoidal structure on the duoidal endomorphism mapping $\infty$-category of a map $\mathcal{O}$-monoidale is equivalent to the convolution product on the mapping $\infty$-category from the dual $\mathcal{O}$-comonoidale to the map $\mathcal{O}$-monoidale. Comment: 35 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.00223 |
| رقم الانضمام: | edsarx.2406.00223 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |