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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.13374 |
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Table of 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.