2014/12/23 by Yann Palu, Palu, Yann
Mathematics · #13F60 #18E30 #18G55 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.CT #math.RT #msc:13F60 #msc:18E30 #msc:18G55
paper · pdf · doi:10.48550/arxiv.1412.7289
arxiv created 2014/12/23 · openalex publication_date 2014/12/23 · arxiv updated 2014/12/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The category of modules over the endomorphism algebra of a rigid object in a Hom-finite triangulated category C has been given two different descriptions: On the one hand, as shown by Osamu Iyama and Yuji Yoshino, it is equivalent to an ideal quotient of a subcategory of C. On the other hand, Aslak Buan and Robert Marsh proved that this module category is also equivalent to some localisation of C. In this paper, we give a conceptual interpretation, inspired from homotopical algebra, of this double description. Our main aim, yet to be acheived, is to generalise Buan-Marsh's result to the case of Hom-infinite cluster categories. We note that, contrary to the more common case where a model category is a module category whose homotopy category is triangulated, we consider here some triangulated categories whose homotopy categories are module categories.