Lefschetz fixed-object and fixed-morphism theorems for acyclic categories
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911834029686784 |
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| author | Castelo-Mourelle, Samuel Macías-Virgós, Enrique Mosquera-Lois, David |
| author_facet | Castelo-Mourelle, Samuel Macías-Virgós, Enrique Mosquera-Lois, David |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06573 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lefschetz fixed-object and fixed-morphism theorems for acyclic categories Castelo-Mourelle, Samuel Macías-Virgós, Enrique Mosquera-Lois, David Algebraic Topology Category Theory 55U10 18B99 37J12 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. |
| title | Lefschetz fixed-object and fixed-morphism theorems for acyclic categories |
| topic | Algebraic Topology Category Theory 55U10 18B99 37J12 |
| url | https://arxiv.org/abs/2404.06573 |