Description:

Title: Parachain complexes

Abstract: Dwyer and Kan found an analogue of the Dold-Kan Theorem, which gives an equivalence between the categories of simplicial objects and chain complexes in an idempotent complete additive category. This extension gives equivalences between the categories of cyclic objects and mixed complexes (graded objects with two anticommuting differentials b and B such that bB+Bb=0), and more generally, between paracyclic objects and parachain complexes (where we only require that 1-bB-Bb is invertible). Paracyclic objects appeared in Boris's first talk, and so this theorem may be of use in investigating the noncommutative Gauss-Manin connection.