On $n$-exact categories I: The existence and uniqueness of maximal $n$-exact structures
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929530475642880 |
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| author | Klapproth, Carlo |
| author_facet | Klapproth, Carlo |
| contents | This paper is the first part of a series that investigates the existence of $n$-exact structures on idempotent complete additive categories for positive integers $n$. It is shown that every idempotent complete additive category has a unique maximal $n$-exact structure. We achieve this by constructing a bijection between $n$-exact structures on a category and certain subcategories of its functor category following ideas of Enomoto. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05242 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $n$-exact categories I: The existence and uniqueness of maximal $n$-exact structures Klapproth, Carlo Category Theory Representation Theory 18A25 (Primary) 18E05, 18G99 (Secondary) This paper is the first part of a series that investigates the existence of $n$-exact structures on idempotent complete additive categories for positive integers $n$. It is shown that every idempotent complete additive category has a unique maximal $n$-exact structure. We achieve this by constructing a bijection between $n$-exact structures on a category and certain subcategories of its functor category following ideas of Enomoto. |
| title | On $n$-exact categories I: The existence and uniqueness of maximal $n$-exact structures |
| topic | Category Theory Representation Theory 18A25 (Primary) 18E05, 18G99 (Secondary) |
| url | https://arxiv.org/abs/2410.05242 |