H. J. Baues, M. Jibladze

Suspension and Loop Objects and Representability of Tracks

In the general setting of groupoid enriched categories, notions of \emph{suspender} and \emph{looper} of a map are introduced, formalizing a generalization of the classical homotopy-theoretic notions of suspension and loop space. The formalism enables subtle analysis of these constructs. In particular, it is shown that the suspender of a principal coaction splits as a coproduct. This result leads to the notion of \emph{theories with suspension} and to the cohomological classification of certain groupoid enriched categories.