The resolving completion of an exact category
Representation Theory
2026-03-16 v1 Category Theory
Abstract
For an exact category we provide two constructions of an ambient category in which the initial category is resolving: In the derived category and in the Gabriel--Quillen embedding. For the first construction we describe a pre-aisle and its right orthogonal using different acyclicty conditions. We provide necessary and sufficient conditions when this pair is a t-structure.
Keywords
Cite
@article{arxiv.2603.13022,
title = {The resolving completion of an exact category},
author = {Marianne Lawson and Janina C. Letz and Julia Sauter},
journal= {arXiv preprint arXiv:2603.13022},
year = {2026}
}
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35 pages