Tuesday, March 03, 14:00, 7.527

Manuel Saorin (Murcia),

Abstract:
In recent papers the authors have used the well-known Hovey correspondence to define model structures on an abelian or weakly idempotent complete Quillen exact category C. In many cases, at the end of the road the authors show that one of the two compatible cotorsion pairs of the Hovey triple is of the form (^⊥W,W^∧), where W is a subcategory such that Extⁱ(W,W')=0, for all i>0 and all W,W'∈W (i.e. W is a self-orthogonal subcategory), and W^∧ denotes the subcategory that consists of the objects Y that admit an exact sequence
0 → W_n → ...→ W₁ → W₀ → Y → 0, with all the W_i∈W. The existence of such a cotorsion pair is equivalent to the condition that W^∧ be special preenveloping and closed under direct summands. In this talk we study this condition for any given self-orthogonal subcategory and show the connection with tilting theory and (relative) Gorenstein homological algebra.