Description:

Title: Parachain complexes

Abstract: The Dold-Kan Theorem gives an equivalence between the categories of simplicial objects and chain complexes in an idempotent complete additive category. Dwyer and Kan found an extension of this theorem, giving 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 this theorem may be of use in investigating the noncommutative Gauss-Manin connection.