Report
Lefschetz fixed-object and fixed-morphism theorems for acyclic categories
| العنوان: | Lefschetz fixed-object and fixed-morphism theorems for acyclic categories |
|---|---|
| المؤلفون: | Castelo-Mourelle, Samuel, Macías-Virgós, Enrique, Mosquera-Lois, David |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Topology, Mathematics - Category Theory, 55U10 18B99 37J12 |
| الوصف: | We introduce two novel complementary notions of the Lefschetz number for a functor from a finite acyclic category to itself and we prove a Lefschetz fixed-object theorem and a Lefschetz fixed-morphism theorem. In order to do so, we use the connection between these type of categories and simplicial structures, such as trisps or delta complexes. Through the use of a pair of functors that, when composed, form the barycentric subdivision, we are not only able to identify fixed objects but also fixed chains of morphisms. Comment: 8 pages with 3 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.06573 |
| رقم الانضمام: | edsarx.2404.06573 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |