chebЧебышевский сборникChebyshevskii Sbornik2226-8383Tula State Lev Tolstoy Pedagogical University10.22405/2226-8383-2020-21-3-29-38cheb-847Research ArticleСтатьиArticleЯдра весовых структур — это в точности слабо идемпотентно полные категорииThe hearts of weight structures are the weakly idempotent complete categoriesБондаркоМихаил ВладимировичBondarkoMikhail Vladimirovich

доктор физико-математических наук, профессор РАН

Doctor of Physical and Mathematical Sciences, RAS Professor

m.bondarko@spbu.ruВостоковСергей ВладимировичVostokovSergei Vladimirovich

доктор физико-математических наук, профессор

Doctor of Physical and Mathematical Sciences, Professor

s.vostokov@spbu.ruСанкт-Петербургский государственный университетРоссияSaint Petersburg State UniversityRussian Federation2020251220202132938Copyright © Бондарко М.В., Востоков С.В., 20202020Бондарко М.В., Востоков С.В.Bondarko M.V., Vostokov S.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.chebsbornik.ru/jour/article/view/847

Мы доказываем, что аддитивные категории, являющиеся ядрами весовых структур —это в точности все слабо идемпотентно полные категории, т. е, категории, в которых расще-пимые мономорфизмы соответствуют прямым слагаемым. Мы также приводим ряд усло-вий, эквивалентных слабой идемпотентной полноте (часть их полностью нова), и обсуж-даем слабо идемпотентные пополнения аддитивных категорий

This paper proves that additive categories that occur as hearts of weight structures areprecisely the weakly idempotent complete categories, that is, the categories where all splitmonomorphisms give direct sum decompositions. The work also gives several other conditionsequivalent to weak idempotent completeness (some of them are completely new) and discussesweak idempotent completions of additive categories

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The authors declare that there are no conflicts of interest present.