Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Xunta de Galicia
Awards: G1496055848, G5296777416
OpenAlex ID: W4394777929