Dear Marco, Many thanks for your explanations, and of course for giving me the possibility to study your book, which I shall do very soon. I have a notion which I hesitated to call directed category for fear of a conflict in using the word directed. Your non technical use of this word encourage me to use it, but I shall first read your book before I make up my mind. Best regards, Jean Le 26 nov. 2013 à 11:11, Marco Grandis a écrit :

Dear Jean,

Presheaves on all finite ordinals are called augmented simplicial sets.

As to 'directed space' I use now this term in a non-technical sense, as referring to any topological structure suitable for directed algebraic topology, like:

- preordered topological space, - d-space, i.e. space with distinguished paths, - c-space, i.e. space with distinguished cubes, - etc.

See my book on 'Directed Algebraic Topology'. Thanks to Cambridge Un. Press, it can be freely (and legally) downloaded from:

http://www.dima.unige.it/~grandis/BkDAT_page.html

(When I first used the term 'directed space', it was equivalent to d- space; later I thought it was better to keep it for a more general meaning.)

Best wishes Marco

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