Triangulation and persistence: Algebra 101
Abstract
This paper lays the foundations of triangulated persistence categories (TPC), which brings together persistence modules with the theory of triangulated categories. As a result we introduce several measurements and metrics on the set of objects of some triangulated categories. We also provide examples of TPCs coming from algebra, algebraic topology, microlocal sheaf theory and symplectic topology.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2021
- DOI:
- arXiv:
- arXiv:2104.12258
- Bibcode:
- 2021arXiv210412258B
- Keywords:
-
- Mathematics - Algebraic Topology;
- Mathematics - Algebraic Geometry;
- Mathematics - Symplectic Geometry;
- 55N31 53D12 (Primary);
- 35A27 (Secondary)