The Euler Characteristic of Finite Categories
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917684627636224 |
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| author | Akkaya, Mustafa Ünlü, Özgün |
| author_facet | Akkaya, Mustafa Ünlü, Özgün |
| contents | We associate a rational number $χ(\mathcal{A})$ to every category $\mathcal{A}$ whose object and morphism sets are finite. We show that the assignment $χ$ is additive under disjoint union and it preserves products. Hence we consider $χ$ as an Euler measure on a family of categories where this assignment also obeys a version of the inclusion--exclusion principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_08966 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Euler Characteristic of Finite Categories Akkaya, Mustafa Ünlü, Özgün Category Theory 18F99, 55U99, 05C50 We associate a rational number $χ(\mathcal{A})$ to every category $\mathcal{A}$ whose object and morphism sets are finite. We show that the assignment $χ$ is additive under disjoint union and it preserves products. Hence we consider $χ$ as an Euler measure on a family of categories where this assignment also obeys a version of the inclusion--exclusion principle. |
| title | The Euler Characteristic of Finite Categories |
| topic | Category Theory 18F99, 55U99, 05C50 |
| url | https://arxiv.org/abs/2301.08966 |