English

Gluing simple-minded collections in triangulated categories

Representation Theory 2024-02-19 v2 Category Theory

Abstract

We provide a technique to glue simple-minded collections along a recollement of Hom-finite Krull-Schmidt triangulated categories over a field. This gluing technique for simple-minded collections is shown to be compatible with those for gluing bounded tt-structures, silting objects, and co-tt-structures in the literature. Furthermore, it also enjoys the properties of preserving partial order and commuting with the operation of mutation.

Keywords

Cite

@article{arxiv.2210.04419,
  title  = {Gluing simple-minded collections in triangulated categories},
  author = {Yongliang Sun and Yaohua Zhang},
  journal= {arXiv preprint arXiv:2210.04419},
  year   = {2024}
}

Comments

23 pages

R2 v1 2026-06-28T03:07:03.302Z