Injectivity paucity in AB5 categories of oversize chains
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915949157810176 |
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| author | Chirvasitu, Alexandru |
| author_facet | Chirvasitu, Alexandru |
| contents | We construct examples of abelian categories with no non-zero injective (or projective) objects satisfying Grothendieck's AB5 condition. The procedure combines Rickard's examples of AB5 categories without products but some non-trivial injectives (also addressing an apparent gap in the literature) with a 2-functorial construct attaching to any category $\mathcal{C}$ that of $\mathcal{C}$-objects equipped with set-indexed families of endomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20554 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Injectivity paucity in AB5 categories of oversize chains Chirvasitu, Alexandru Category Theory Rings and Algebras 18E10, 18G05, 18A35, 18A30, 18A20, 18N10, 18E40, 03E10 We construct examples of abelian categories with no non-zero injective (or projective) objects satisfying Grothendieck's AB5 condition. The procedure combines Rickard's examples of AB5 categories without products but some non-trivial injectives (also addressing an apparent gap in the literature) with a 2-functorial construct attaching to any category $\mathcal{C}$ that of $\mathcal{C}$-objects equipped with set-indexed families of endomorphisms. |
| title | Injectivity paucity in AB5 categories of oversize chains |
| topic | Category Theory Rings and Algebras 18E10, 18G05, 18A35, 18A30, 18A20, 18N10, 18E40, 03E10 |
| url | https://arxiv.org/abs/2604.20554 |