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Preprints, Working Papers, ... Year : 2021

On analytic contravariant functors on free groups

Abstract

Working over a field $k$ of characteristic zero, the category of analytic contravariant functors on the category of finitely-generated free groups is shown to be equivalent to the category of representations of the $k$-linear category associated to the Lie operad. The proof uses the original Ginzburg-Kapranov approach to Koszul duality of binary quadratic operads. The equivalence is made explicit using the $k$-linear category associated to the operad encoding unital associative algebras, which provides the appropriate `twisting bimodule'.

Dates and versions

hal-03367098 , version 1 (06-10-2021)

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Geoffrey Powell. On analytic contravariant functors on free groups. 2021. ⟨hal-03367098⟩
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