Gluing simple-minded collections in triangulated categories
Yongliang Sun, Yaohua Zhang

TL;DR
This paper introduces a new technique for combining simple-minded collections in triangulated categories, ensuring compatibility with existing structures and preserving key properties like order and mutation.
Contribution
It develops a novel gluing method for simple-minded collections that aligns with known techniques for $t$-structures, silting objects, and co-$t$-structures, enhancing the understanding of their interplay.
Findings
The gluing technique is compatible with existing structures.
It preserves partial order among collections.
It commutes with mutation operations.
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 -structures, silting objects, and co--structures in the literature. Furthermore, it also enjoys the properties of preserving partial order and commuting with the operation of mutation.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Rings, Modules, and Algebras
