Simple objects in the heart of a tt-structure

We give some conditions for objects X0,…,XrX0,…,Xr to be what we call a “cohomologically Schurian set of generators” for the bounded derived category DbDb(ΛΛ-mod) of a finite-dimensional algebra ΛΛ. For any such set of generators, we construct a tt-structure on DbDb(ΛΛ-mod), which has these objects as its simple objects. If ΛΛ is self-injective, we prove that the heart of this tt-structure is equivalent to a module category. To prove this fact we prove that the heart has an injective cogenerator.