The hearts of weight structures are the weakly idempotent complete categories
Category Theory
2020-05-26 v1 K-Theory and Homology
Representation Theory
Abstract
In this note we prove that additive categories that occur as hearts of weight structures are precisely the weakly idempotent completecategories, that is, the categories where all split monomorphisms give direct sum decompositions. We also give several other conditions equivalent to weak idempotent completeness (some of them are completely new), and discuss weak idempotent completions of additive categories.
Keywords
Cite
@article{arxiv.2005.11518,
title = {The hearts of weight structures are the weakly idempotent complete categories},
author = {Mikhail V. Bondarko and Sergei V. Vostokov},
journal= {arXiv preprint arXiv:2005.11518},
year = {2020}
}
Comments
13 pages; comments are very welcome!