nomenclature is better so will adopt it) and show how that theory links in with some old ideas of Boardman and Vogt, Dwyer and Kan, and Cordier and myself;

-   To ask lots of questions of myself and of the reader.

The notes include some material from the ‘Cubo’ article, [@cubo], which was itself based on notes for a course at the *Corso estivo Categorie e Topologia* in 1991, but the overlap has been kept as small as is feasible as the purpose and the audience of the two sets of notes are different and the abstract homotopy theory has ‘moved on’, in part, to try the new methods out on those same ‘old’ problems and to attack new ones as well.

As usual when you try to specify ‘learning outcomes’ you end up asking who has done the learning, the audience? Perhaps. The lecturer, most certainly!

**Acknowledgements**

I would like to thank Heiner Kamps and his colleagues at the Fern Univeristät for the invitation to give the talks of which these notes are a summary and to the Fern Univeristät for the support that made the visit possible, to José Manuel García-Calcines, Josué Remedios and their colleagues and for 