Abstract
We study the derived invariance of the cohomology theories Hoch*, H* and HC* associated with coalgebras over a field. We prove a theorem characterizing derived equivalences. As particular cases, it describes the two following situations: (1) f: C→D a quasi-isomorphism of differential graded coalgebras, (2) the existence of a ‘cotilting’ bicomodule C T D . In these two cases we construct a derived-Morita equivalence context, and consequently we obtain isomorphisms Hoch*(C)≅Hoch*(D) and H*(C)≅H*(D). Moreover, when we have a coassociative map inducing an isomorphism H*(C)≅H*(D) (for example, when there is a quasi-isomorphism f: C→D), we prove that HC*(C)≅HC*(D).
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