Dear Marco, Just two questions about terminology: You say that presently the term of simplicial set/object seems to be generally accepted (for a presheaf on positive finite ordinals) I suppose that by positive you mean non- empty. Is there an adopted name for presheaves on all finite ordinals (including the empty one) Among the distinctions you make there is: space/directed space. I'm not sure I know what a directed space is. Could you please tell me what a directed space is. Best wishes, Jean Le 25 nov. 2013 à 10:11, Marco Grandis a écrit :
Dear Bill,
The history of simplicial terms is certainly complicated and often contradictory. Presently, the term of 'simplicial set/object' seems to be generally accepted (for a presheaf on positive finite ordinals) and this notion seems to be mostly considered as the leading one in its framework. My modest opinion is that simplicial terminology should be organised taking this term as the leading one.
It does not seem accurate to consider that there is an "opposition "between the ordered and unordered cases.
Fine, I agree, I should replace 'opposition' with 'distinction'. Certainly, I would not speak of opposition for the relationships set / preordered set space / directed space classical algebraic topology / directed algebraic topology.
Your comments on distributive lattices are most interesting.
Best wishes Marco
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]