This paper proves that additive categories that occur as hearts of weight structures are precisely the weakly idempotent complete categories, that is, the categories where all split monomorphisms give direct sum decompositions. The work also gives several other conditions equivalent to weak idempotent completeness (some of them are completely new) and discusses weak idempotent completions of additive categories.
|Translated title of the contribution||The hearts of weight structures are the weakly idempotent complete categories|
|Number of pages||10|
|State||Published - 2020|
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