Infinity-tilting theory

0508627 - MÚ 2020 RIV US eng J - Journal Article
Positselski, Leonid - Šťovíček, J.
Infinity-tilting theory.
Pacific Journal of Mathematics. Roč. 301, č. 1 (2019), s. 297-334. ISSN 0030-8730
Institutional support: RVO:67985840
Keywords : tilting theory * Wakamatsu tilting module * pseudo-derivedequivalence
OECD category: Pure mathematics
Impact factor: 0.697, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.2140/pjm.2019.301.297

We define the notion of an infinitely generated tilting object of infinite homologicaldimension in an abelian category. A one-to-one correspondence between ∞-tiltingobjects in complete, cocomplete abelian categories with an injective cogenerator and ∞-cotilting objects incomplete, cocomplete abelian categories with a projective generator is constructed. We also introduce ∞-tilting pairs, consistingof an ∞-tilting objectand its ∞-tiltingclass, and obtain a bijective correspondence between ∞-tilting and ∞-cotiltingpairs. Finally, we discuss the related derived equivalences and t-structures.
Permanent Link: http://hdl.handle.net/11104/0299482