2017/11/30 by Leonid Positselski, Jan Stovicek · 3 citations
Mathematics · #math.CT #math.RT
paper · pdf · doi:10.2140/pjm.2019.301.297
published as Pacific J. Math. 301 (2019) 297-334 · LaTeX 2e with pb-diagram and xy-pic, 34 pages, 4 figures; v.3: minor corrections, references updated
arxiv created 2019/08/13 · arxiv updated 2019/09/18
We define the notion of an infinitely generated tilting object of infinite homological dimension in an abelian category. A one-to-one correspondence between ∞-tilting objects in complete, cocomplete abelian categories with an injective cogenerator and ∞-cotilting objects in complete, cocomplete abelian categories with a projective generator is constructed. We also introduce ∞-tilting pairs, consisting of an ∞-tilting object and its ∞-tilting class, and obtain a bijective correspondence between ∞-tilting and ∞-cotilting pairs. Finally, we discuss the related derived equivalences and t-structures.