تقرير
Taut functors and the difference operator
| العنوان: | Taut functors and the difference operator |
|---|---|
| المؤلفون: | Paré, Robert |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Category Theory |
| الوصف: | We establish a calculus of differences for taut endofunctors of the category of sets, analogous to the classical calculus of finite differences for real valued functions. We study how the difference operator interacts with limits and colimits as categorical versions of the usual product and sum rules. The first main result is a lax chain rule which has no counterpart for mere functions. We also show that many important classes of functors (polynomials, analytic functors, reduced powers, ...) are taut, and calculate explicit formulas for their differences. Covariant Dirichlet series are introduced and studied. The second main result is a Newton summation formula expressed as an adjoint to the difference operator. Comment: 80 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.21129 |
| رقم الأكسشن: | edsarx.2407.21129 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |