On tilting complexes providing derived equivalences that send simple-minded objects to simple objects

Given a set of 'simple-minded' objects in a derived category, Rickard constructed a complex, which over a symmetric algebra provides a derived equivalence sending the 'simple-minded' objects to simple ones. We characterise in terms of t-structures, when this complex is a tilting complex, show that there is an associated natural $t$-structure and we provide an alternative construction of this complex in terms of A-infinity-structures. Our approach is similar to that of Keller--Nicolás.

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