Balanced systems for $\mathrm{Hom}$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866917575571537920 |
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| author | Becerril, Víctor Mendoza, Octavio Pérez, Marco A. |
| author_facet | Becerril, Víctor Mendoza, Octavio Pérez, Marco A. |
| contents | From the notion of (co)generator in relative homological algebra, we present the concept of finite balanced system $[(\mathcal{X} , ω); (ν, \mathcal{Y})]$ as a tool to induce balanced pairs $(\mathcal{X} , \mathcal{Y} )$ for the $\mathrm{Hom}$ functor with domain determined by the finiteness of homological dimensions relative to $\mathcal{X}$ and $\mathcal{Y}$.
This approach to balance will cover several well known ambients where right derived functors of $\mathrm{Hom}$ are obtained relative to certain classes of objects in an abelian category, such as Gorenstein projective and injective modules and chain complexes, Gorenstein modules relative to Auslander and Bass classes, among others. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_12140 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Balanced systems for $\mathrm{Hom}$ Becerril, Víctor Mendoza, Octavio Pérez, Marco A. Category Theory 18G10, 18F20, 16E30, 16E65 From the notion of (co)generator in relative homological algebra, we present the concept of finite balanced system $[(\mathcal{X} , ω); (ν, \mathcal{Y})]$ as a tool to induce balanced pairs $(\mathcal{X} , \mathcal{Y} )$ for the $\mathrm{Hom}$ functor with domain determined by the finiteness of homological dimensions relative to $\mathcal{X}$ and $\mathcal{Y}$. This approach to balance will cover several well known ambients where right derived functors of $\mathrm{Hom}$ are obtained relative to certain classes of objects in an abelian category, such as Gorenstein projective and injective modules and chain complexes, Gorenstein modules relative to Auslander and Bass classes, among others. |
| title | Balanced systems for $\mathrm{Hom}$ |
| topic | Category Theory 18G10, 18F20, 16E30, 16E65 |
| url | https://arxiv.org/abs/2203.12140 |