Gluing simple-minded collections in triangulated categories

Yongliang Sun, Yaohua Zhang

Published 2022-10-10, updated 2024-02-16Version 2

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 $t$-structures, silting objects, and co-$t$-structures in the literature. Furthermore, it also enjoys the properties of preserving partial order and commuting with the operation of mutation.