تقرير
An $\mathcal{O}$-monoidal Grothendieck construction
| العنوان: | An $\mathcal{O}$-monoidal Grothendieck construction |
|---|---|
| المؤلفون: | Haderi, Redi, Stern, Walker H. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Category Theory, 18N10 (primary), 18M60 (secondary) |
| الوصف: | Given an operad $\mathcal{O}$, we define a notion of weak $\mathcal{O}$-monoids -- which we term $\mathcal{O}$-pseudomonoids -- in a 2-category. In the special case with the 2-category in question is the 2-category $\mathsf{Cat}$ of categories, this yields a notion of $\mathcal{O}$-monoidal category, which in the case of the associative and commutative operads retrieves unbiased notions of monoidal and symmetric monoidal categories, respectively. We carefully unpack the definition of $\mathcal{O}$-monoids in the 2-categories of discrete fibrations and of category-indexed sets. Using the classical Grothendieck construction, we thereby obtain an $\mathcal{O}$-monoidal Grothendieck construction relating lax $\mathcal{O}$-monoidal functors into Set to strict $\mathcal{O}$-monoidal functors which are also discrete fibrations. Comment: 37 pages. Comments welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.01031 |
| رقم الأكسشن: | edsarx.2404.01031 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |