Communication Dans Un Congrès Année : 2024

Some Applications of Extriangulated Categories

Résumé

Extriangulated categories axiomatise extension-closed subcategories of triangulated categories and generalise both exact categories and triangulated categories. This survey article presents three applications of extriangulated categories to homotopical algebra, algebraic combinatorics and representation theory. The first shows that, via some generalised Hovey's correspondence, extriangulated categories easily give rise to model category structures with triangulated homotopy categories. As a second application, extriangulated structures play a fundamental role in the construction of polytopal realisations of g-vector fans. This allows for a generalisation of ABHY's construction appearing in the study of scattering amplitudes in theoretical physics. Lastly, extriangulated categories provide a convenient framework for studying mutations in representation theory and flips in algebraic combinatorics. In nice enough hereditary extriangulated categories, there is a well-behaved theory of mutation for silting objects, which encompass cluster tilting, two-term silting, relative tilting, mutation of maximal almost-rigid modules, flip of dissections and mutation of intermediate co-t-structures.

HAL

Est une version de hal-04539621 Preprint Yann Palu. Some applications of extriangulated categories. 2024. ⟨hal-04539621⟩

Fichier non déposé

Dates et versions

hal-04852197 , version 1 (20-12-2024)

Identifiants

Citer

Yann Palu. Some Applications of Extriangulated Categories. Abel Symposium on Triangulated Categories in Representation Theory and Beyond, Jun 2022, Alesund, Norway. pp.217-254, ⟨10.1007/978-3-031-57789-5_8⟩. ⟨hal-04852197⟩
36 Consultations
0 Téléchargements

Altmetric

Partager

  • More