Luisa Fiorot
Universidade de Pádua

Abstract: Bondal and Van den Bergh have constructed an equivalence between the notion of quasi-abelian category studied by Schneiders and that of tilting torsion pair on an abelian category. We will provide an overview of this result and hence we will extend this picture into a hierarchy of n-quasi-abelian categories and n-tilting torsion classes.
In particular 0-quasi-abelian categories are abelian categories, 1-quasi-abelian categories are Schneiders quasi-abelian categories, 2-quasi-abelian categories are additive categories admitting kernels and cokernels. Any n-quasi-abelian category E admits a “derived” category endowed with two canonical t-structures (the left and the right one) such that E coincides with the intersection of their hearts.

This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.