تقرير
2-derivators
| العنوان: | 2-derivators |
|---|---|
| المؤلفون: | Di Vittorio, Nicola |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Category Theory, Mathematics - Algebraic Topology, 18N40 18N65 55U35 |
| الوصف: | Introduced independently by Grothendieck and Heller in the 1980s, derivators provide a formal way to study homotopy theories by working in some quotient category such as the homotopy category of a model category. In 2015 Riehl and Verity introduced $\infty$-cosmoi, which are particular $(\infty,2)$-categories where one can develop $(\infty,1)$-category theory in a synthetic way. They noticed that much of the theory of $\infty$-cosmoi can be developed inside a quotient, the homotopy $2$-category. In the following, we begin a program that aims to formalise the $\infty$-cosmological approach to $\infty$-category theory in a derivator-like framework. In this paper we introduce some axioms and demonstrate they hold in a variety of models, including common models related to $\infty$-category theory. We also prove that these axioms are stable under a particular shift operation. Comment: 48 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2309.05216 |
| رقم الأكسشن: | edsarx.2309.05216 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |