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As far as I am concerned, you may indeed feel free to remove these category labels. As I mentioned before and as you notice here, they have never been in wide-spread systematic use anyways (while instead the floating context menus have been).
Just to notice that the reasons you give here for removing the label don’t seem to be sensible to me:
There is no “cycle” here, is there?
If there is really only one entry with category “category theory” and if you care about the category-system, then the conclusion would be to add that label to all other entries on category theory.
There is no pleonasm here. (Or maybe you are joking?)
I appreciate if you and others feel energetic about cleaning up this bit of the nLab. Let’s just make sure we all understand what’s going on:
A few users have experimented, in the past, with using Instiki’s category-functionality for organizing entries into topic clusters. Since, however, this functionality just provides users with a blindly ordered list of links (which, when long, is hard to read and hence hard to take hints from) others have instead used floating context menus of related entries (which may be formatted nicely such as to be more helpful to the reader – on Wikipedia they have similar boxes for collecting pointers to related entries). As far as I am aware, the latter has found wide-spread systematic use, mainly because that’s the system that I have adopted.
Of course both systems can exist in parallel.
Anyone energetic about cleaning up the nLab who thinks the category-labels are more or as useful than the floating context menus should add loads of them. Every single entry on category theory should have a label category: category theory, so that they are actually all grouped and linked together this way.
Anyone energetic about cleaning up the nLab who thinks the category-labels are less useful and potentially misleading as long as they are incomplete should go and remove them all, and instead replace them with usefully organized and nicely formatted floating context menus.
The best solution would be if somebody with some coding skill could look into this. If a category-label in the source would automatically trigger the appearance of a nicely formatted floating context menu, that would finally be the solution that combines the idea of automated context (which must have driven the Instiki programmers who introduced that category-functionality) while improving it to the degree that it becomes actually useful on a larger Wiki (which the Instiki developers don’t seem to have anticipated).
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