#### Vol. 301, No. 1, 2019

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$\infty$-tilting theory

### Leonid Positselski and Jan Šťovíček

Vol. 301 (2019), No. 1, 297–334
##### Abstract

We define the notion of an infinitely generated tilting object of infinite homological dimension in an abelian category. A one-to-one correspondence between $\infty$-tilting objects in complete, cocomplete abelian categories with an injective cogenerator and $\infty$-cotilting objects in complete, cocomplete abelian categories with a projective generator is constructed. We also introduce $\infty$-tilting pairs, consisting of an $\infty$-tilting object and its $\infty$-tilting class, and obtain a bijective correspondence between $\infty$-tilting and $\infty$-cotilting pairs. Finally, we discuss the related derived equivalences and t-structures.

##### Keywords
tilting theory, Wakamatsu tilting module, pseudo-derived equivalence
##### Mathematical Subject Classification 2010
Primary: 18E10, 18E30
Secondary: 16E30