On cohomological periodicity for infinite groups.
It is shown that the categories of -coalgebras for a commutative unital ring and the category of -corings for some -algebra as well as their respective categories of comodules are locally presentable.
We classify, up to derived (equivalently, tilting-cotilting) equivalence, all nondegenerate gentle two-cycle algebras. We also give a partial classification and formulate a conjecture in the degenerate case.