On the classification of F-fibrations

We begin this paper by studying the construction of principal fibrations associated to F-fibrations (that is to say, fibrations whose fibres are objects of a fixed category F). We prove that under certain conditions we can even define an inverse construction (in the sense of May-Stasheff). Finally, with the aid of the Dold-Lashof-Fuchs classification theorem, we give a classification theorem for numerable F-fibrations. The paper is developed entirely within the framework of the category of k-spaces.