Admissible intersection and sum property

Souheila Hassoun; Sunny Roy

Admissible intersection and sum property

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arxiv 1906.03246 v3 pith:HO7MO25K submitted 2019-06-07 math.RT math.CTmath.RA

Souheila Hassoun , Sunny Roy This is my paper · ORCID

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keywords categoriesadmissibleexactabeliancharacterisationscontextgeneralisegive

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We introduce subclasses of exact categories in terms of admissible intersections or admissible sums or both at the same time. These categories are recently studied by Br\"ustle, Hassoun, Shah, Tattar and Wegner to give characterisations of quasi-abelian and abelian categories. We also generalise the Schur lemma to the context of exact categories.

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The Jordan-H\"older property and Grothendieck monoids of exact categories
math.RT 2019-08 accept novelty 7.0 of 10

An exact category satisfies the Jordan-Hölder property if and only if its Grothendieck monoid is free, with a rank-counting criterion and a permutation-combinatorics application to type A quivers.

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