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1. I decided that nLab is probably a better place to develop my ideas than ‘wikipedia’, where I posted one article on this topic but never felt confident to add more, since wikipedia is not really meant for ’ongoing research’. I really liked the idea of using this space for ’public notes on my research’ and am looking forward to getting reactions from some of you.

As a starter, I feel that using the first-person form in my reporting is more ’honest’ regarding the academic status of the piece. Prefix orders are not an accepted notion in literature yet, I think. The notion itself is used often, but always in a specific context and was (as far as I know) never generalized - until now…

Pieter Cuijpers

2. Hi Pieter, I imagine that people will probably wish to discuss this page, to see to what it extent it follows what was suggested by David C here. (I appreciate that you may have created this page before seeing David C’s post). Maybe you could hold off with further edits close to your personal research until you get some feedback about that? The edit that you made to tree was fine; the only thing people might wish to discuss there is again the reference to your own page. But it might be fine, given that your work is published; I’ll let others decide that :-).

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeFeb 1st 2019
• (edited Feb 1st 2019)

[ overlapped with Richard’s message ]

It’s good practice to indicate whether a concept on an $n$Lab page is traditional in the literature or something being introduced on the page, but the first person paragraphs you have now may be a little confusing, since the reader who doesn’t go through the trouble of inspecting the history of the page does not know who it is who is speaking.

I suggest to slightly reorganize as follows:

The very first sentence of an Idea-section should just say what the concept is that is going to be discussed, right on the point, without motivation or history. I suppose the first sentence here could be something like:

By a prefix order we mean a partial order which is downwards totally ordered.

(or whatever is the best informal description).

Then after that there can usefully follow sentences like “Beware that this terminology is not widely established at the moment. It was introduced in Cuijpers 13 in order to account for the relevance of such kinds of orders in the semantics of certain programming languages” or the like.

By the way, do you need help with formatting references, or do you know how to fomat them and just haven’t gotten around to yet?

3. Urs’ suggestions sound great.

• CommentRowNumber5.
• CommentAuthorPieter
• CommentTimeFeb 2nd 2019
Thanks Richard and Urs, that sounds like a good way to indicate in a "neutral" way what the academic status of the page is.
I'll update it as soon as I get round to it. First, some classes need to be prepared...

I could use a little help on references. I simply didn't take the time yet to figure out what the syntax is for them exactly.
But only if it is not too much trouble, I will come around to it eventually (after the start of the semester has passed, I imagine).

Regarding "original work" I'll stick to things I've already published for the time being, and try to get responses to the rest on the forum first.
Having a personal page to use as an actual notebook in due time would be helpful, I expect. But let's first see if this way of working "sticks".
Category theory is just a side-job for me ;-)
• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeFeb 2nd 2019

formatted the references, made the intro-paragraphs hyperlink to them, and slightly adjusted wording, as we discussed (but just a suggestion, please edit as need be)

4. Fixed a syntax error (left backticks cannot be used as quotation marks, because they indicate start of a code block).

• CommentRowNumber8.
• CommentAuthorTim_Porter
• CommentTimeFeb 3rd 2019

Fixed spelling error in first line.