The cyclic bar construction on A_\infty Hspaces
Abstract
We set up a general framework for enriching a subcategory of the category of noncommutative sets over a category C using products of the objects of a non\Sigma operad P in \C. By viewing the simplicial category as a subcategory of the category of noncommutative sets in two different ways, we obtain two generalizations of simplicial objects. For the operad given by the Stasheff associahedra we obtain a model for the 2sided bar construction in the first case and the cyclic bar and cobar construction in the second case. Using either the associahedra or the cyclohedra in place of the geometric simplices we can define the geometric realization of these objects.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2006
 arXiv:
 arXiv:math/0612165
 Bibcode:
 2006math.....12165A
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Category Theory;
 55R35;
 18D50
 EPrint:
 24 pages, 8 figures