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Abstract It is proved that any tilting adjunction is completely described by an exact category with a coherence property and the closure condition that exact sequences are acyclic. The coherence… Click to show full abstract
Abstract It is proved that any tilting adjunction is completely described by an exact category with a coherence property and the closure condition that exact sequences are acyclic. The coherence property signifies that two associated categories where the tilting adjunction takes place are abelian. The adjoint pair is then obtained in a unique fashion. Applications to tilting between module categories, n-tilting modules, tilting from cotorsion pairs, and Wakamatsu tilting modules, are given. Criteria for triangle equivalences induced by the derived functors between unbounded derived categories are established.
Journal Title: Communications in Algebra
Year Published: 2021
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