2009/03/16 by Vincent Beck, Beck, Vincent
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #math.CT #math.RT #msc:18E10 #msc:18E30
paper · pdf · doi:10.48550/arxiv.0903.2868
arxiv created 2009/03/16 · arxiv updated 2009/12/01
Let \Ascr,\Bscr be exact categories with \Ascr karoubian and M be an exact functor. Under suitable adjonction hypotheses for M, we are able to show that the direct factors of the objects of \Ascr of the form MY with Y ∈ \Bscr make up a Frobenius category which allow us to define an M-stable category for \Ascr only by quotienting. In addition, we propose a construction of an M-stable category for \Ascr,\Bscr triangulated categories and M a triangulated functor. We illustrate this notion with a theorem of Keller and Vossieck which links the two notions of M-stable category.