Fibrant diagrams, rectifications and a construction of loday

AbstractThe notion of a fibrant diagram was introduced by Edwards and Hastings. The limit of a fibrant diagram coincides with its homotopy limit. A process of rectification of homotopy coherent diagrams has been introduced by the authors. The homotopy limit of a coherent diagram is the limit of its rectification. In this paper we show that the rectified diagrams are fibrant and we give applications to homotopy limits and also to a construction of a catn-group from a homotopy coherent n-cube of spaces