Approximating triangulated categories by spaces
Category Theory
2023-04-25 v3 Algebraic Geometry
Algebraic Topology
Representation Theory
Abstract
We initiate a systematic study of lattices of thick subcategories for arbitrary essentially small triangulated categories. To this end we give several examples illustrating the various properties these lattices may, or may not, have and show that as soon as a lattice of thick subcategories is distributive it is automatically a spatial frame. We then construct two non-commutative spectra, one functorial and one with restricted functoriality, that give universal approximations of these lattices by spaces.
Cite
@article{arxiv.2205.13356,
title = {Approximating triangulated categories by spaces},
author = {Sira Gratz and Greg Stevenson},
journal= {arXiv preprint arXiv:2205.13356},
year = {2023}
}
Comments
Further minor updates, accepted for publication in Advances in Mathematics