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Derived Mackey functors

SPEAKER: Dmitry Kaledin

TITLE: Derived Mackey functors

ABSTRACT Assume given a finite group G. It has been long understood by algebraic topologists that the proper target for G-equivariant homology functors are not just abelian groups equipped with a G-action, but some much more elaborate gadgets called “Mackey functors”. G-Mackey functors form an abelian category M(G). One could expect that equivariant homology lifts to a functor with values in the derived category D(M(G)), but as it turns out, this is not the case: the natural target for the DG version of equivariant homology is a different triangulated category DM(G); it contains M(G) but differs from D(M(G)). I am going to present the construction of this category DM(G) and describe some of its very nice properties. Although the main motivation comes from topology, the whole subject can be treated as an exercize in homological algebra with no relation to its topological origin.