Algebra & Topology Seminar

Monday 18/5, M2 and online

10.00-11.00 Anastasios Slaftsos (University of Padova), Varying exact structures in additive categories

Abstract: In the additive category of complexes over a ring, one can consider various exact structures. In particular, considering the abelian structure, yields an abelian model structure whose homotopy category is nothing more than the derived category of the ring, whereas endowing complexes with the degreewise split exact structure leads to an exact model structure whose homotopy category is the homotopy category of complexes. In this example, it is well known that the inclusion of the degreewise split exact structure to the abelian one, induces a Verdier localisation between the two homotopy categories. In this talk, we investigate analogous phenomena in additive categories endowed with well behaved exact structures. As an application we recover the Q-shaped derived category of Holm and Jorgensen and construct an intermediate Q-shaped homotopy category, analogous to the homotopy category of complexes. Finally, we show that the Q-shaped derived category is a Verdier quotient of the Q-shaped homotopy category, and that this quotient functor is part of recollement, generalising results of Verdier and Krause. This talk is based on a joint work with Jorge Vitória (arxiv:2602.22986).