2011/11/08 by Nakaoka, Hiroyuki
#Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1111.1820
In our previous article, we constructed an abelian category from any torsion pair on a triangulated category. This generalizes the heart of a t-structure and the ideal quotient by a cluster tilting subcategory. Recently, generalizing the quotient by a cluster tilting subcategory, Buan and Marsh showed that an integral preabelian category can be constructed as a quotient, from a rigid object in a triangulated category with some conditions. In this article, by considering a pair of torsion pairs, we make a simultaneous genralization of these two constructions.