On pure monomorphisms and pure epimorphisms in accessible categories
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911416911396864 |
|---|---|
| author | Positselski, Leonid |
| author_facet | Positselski, Leonid |
| contents | In all $κ$-accessible additive categories, $κ$-pure monomorphisms and $κ$-pure epimorphisms are well-behaved, as shown in our previous paper arXiv:2311.02418. This is known to be not always true in $κ$-accessible nonadditive categories. Nevertheless, mild assumptions on a $κ$-accessible category are sufficient to prove good properties of $κ$-pure monomorphisms and $κ$-pure epimorphisms. In particular, in a $κ$-accessible category with finite products, all $κ$-pure monomorphisms are $κ$-directed colimits of split monomorphisms, while in a $κ$-accessible category with finite coproducts, all $κ$-pure epimorphisms are $κ$-directed colimits of split epimorphisms. We also discuss what we call Quillen exact classes of monomorphisms and epimorphisms, generalizing the additive concept of one-sided exact category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13374 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On pure monomorphisms and pure epimorphisms in accessible categories Positselski, Leonid Category Theory In all $κ$-accessible additive categories, $κ$-pure monomorphisms and $κ$-pure epimorphisms are well-behaved, as shown in our previous paper arXiv:2311.02418. This is known to be not always true in $κ$-accessible nonadditive categories. Nevertheless, mild assumptions on a $κ$-accessible category are sufficient to prove good properties of $κ$-pure monomorphisms and $κ$-pure epimorphisms. In particular, in a $κ$-accessible category with finite products, all $κ$-pure monomorphisms are $κ$-directed colimits of split monomorphisms, while in a $κ$-accessible category with finite coproducts, all $κ$-pure epimorphisms are $κ$-directed colimits of split epimorphisms. We also discuss what we call Quillen exact classes of monomorphisms and epimorphisms, generalizing the additive concept of one-sided exact category. |
| title | On pure monomorphisms and pure epimorphisms in accessible categories |
| topic | Category Theory |
| url | https://arxiv.org/abs/2506.13374 |