Intersections, sums, and the Jordan-H\"older property for exact categories Article Swipe
We investigate how the concepts of intersection and sums of subobjects carry to exact categories. We obtain a new characterisation of quasi-abelian categories in terms of admitting admissible intersections in the sense of Hassoun and Roy. There are also many alternative characterisations of abelian categories as those that additionally admit admissible sums and in terms of properties of admissible morphisms. We then define a generalised notion of intersection and sum which every exact category admits. Using these new notions, we define and study classes of exact categories that satisfy the Jordan-H\"older property for exact categories, namely the Diamond exact categories and Artin-Wedderburn exact categories. By explicitly describing all exact structures on $\mathcal{A}= \mbox{rep}\, \Lambda$ for a Nakayama algebra $\Lambda$ we characterise all Artin-Wedderburn exact structures on $\mathcal{A}$ and show that these are precisely the exact structures with the Jordan-H\"{o}lder property.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2006.03505
- https://arxiv.org/pdf/2006.03505
- OA Status
- green
- Cited By
- 1
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4287762082
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4287762082Canonical identifier for this work in OpenAlex
- Title
-
Intersections, sums, and the Jordan-H\"older property for exact categoriesWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2020Year of publication
- Publication date
-
2020-06-05Full publication date if available
- Authors
-
Thomas Brüstle, Souheila Hassoun, Aran TattarList of authors in order
- Landing page
-
https://arxiv.org/abs/2006.03505Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2006.03505Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2006.03505Direct OA link when available
- Concepts
-
Mathematics, Morphism, Intersection (aeronautics), Abelian group, Property (philosophy), Exact sequence, Exact solutions in general relativity, Pure mathematics, Algebra over a field, Combinatorics, Mathematical analysis, Engineering, Aerospace engineering, Epistemology, PhilosophyTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
-
2022: 1Per-year citation counts (last 5 years)
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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