Operadic homology and functor homology

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This project lies in algebraic topology and homotopical algebra. It studies approaches todihedral (co)homology and related homology theories. The aim is to compare the various approaches in the litterature and to extend these, where needed, to suitable infinity versions of algebras. The approach taken is likely to involve tools from operads and from functor homology. It should give a conceptual framework where properties such as homotopy invariance are built in rather than a matter of checking formulas. The algebraic structure of these (co)homology theories will also be investigated.