Abelian and model structures on tame functors
Fuente:
arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914725199085568 |
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| author | Chachólski, Wojciech Giunti, Barbara Landi, Claudia Tombari, Francesca |
| author_facet | Chachólski, Wojciech Giunti, Barbara Landi, Claudia Tombari, Francesca |
| contents | In this paper, we discuss certain circumstances in which the category of tame functors inherits an abelian category structure with minimal resolutions and a model category structure with minimal cofibrant replacements. We also present a structure theorem for cofibrant objects in the category of tame functors indexed by realizations of posets of dimension $1$ with values in the category of chain complexes in an abelian category whose all objects are projectives. Moreover, we introduce a general technique to generate indecomposable objects in the abelian category of functors indexed by finite posets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_04079 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Abelian and model structures on tame functors Chachólski, Wojciech Giunti, Barbara Landi, Claudia Tombari, Francesca Algebraic Topology In this paper, we discuss certain circumstances in which the category of tame functors inherits an abelian category structure with minimal resolutions and a model category structure with minimal cofibrant replacements. We also present a structure theorem for cofibrant objects in the category of tame functors indexed by realizations of posets of dimension $1$ with values in the category of chain complexes in an abelian category whose all objects are projectives. Moreover, we introduce a general technique to generate indecomposable objects in the abelian category of functors indexed by finite posets. |
| title | Abelian and model structures on tame functors |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2301.04079 |