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It’s come up time and time again that HoTT Wiki and nlab should be more linked or less linked. I have created this post to finally settle the issue.
I personally propose that HoTT wiki stands on its own, and can also link to the nlab. But it shouldn’t rely on the nlab to explain things. I believe the (not explicitly mentioned) point of HoTT Wiki is to be an accumulation of mathematics in HoTT and essentially a proof of concept. It has the potential to have a much wider reach than the HoTT book can (for obvious reasons) and I forsee it being a useful tool for researchers in HoTT as reference and knowledge.
This doesn’t come without issues however: nlab has a vast amount of content on HoTT and this would cause a lot of duplication. Especially in the future when newer articles are added to HoTT wiki and not to nlab. But part of this issue is because HoTT wiki is in its infancy, thus nlab cannot really rely on linking to it.
Another point I want to make is that HoTT wiki shouldn’t necesserily be about the npov. But rather doing mathematics with oo-groupoids. There is of course a lot of potential for HoTT to interact with the npov and I think that should really be the subject of nlab HoTT rather than the HoTT wiki.
Of course these are all my opinions and I would love to hear some ayes and neys on this subject. And for this post to serve as a future reference for those confused about this topic.
Good that you are energetic about editing the HoTT wiki, that’s the most important ingredient. Experience shows that most design choices are hard to anticipate, yet harder to discuss pre-emptively, but will sort themselves out in the process of editing.
Duplication is not that bad and is not a pressing issue at this stage of development anyway.
Just make sure all relevant articles do point to each other recognizably, so that the reader can find the information. Better the reader sees something of relevance twice, than not seeing it at all.
Once the HoTT wiki has matured a bit, we will have plenty of time and occasion to see if we want to harmonize given pairs of entries here and there.
I agree with pretty much all of that. To be honest, some of the HoTT material on the nLab is out of date or misleading anyway; it will be good to approach each subject freshly from the “HoTT PoV”.
100% agree as well! Most important thing is that you have the energy to add the material, that’s great!
Alitzer, I think you are doing great work. I see part of the work is copying relevant material from the HoTT book. In fact, the HoTT book has been wiki-fied. Richard, does it make sense to have a similar hyperlinked version of the HoTT book included in the nlab. I don’t assume this has an easy answer, but I know some of the people (Joe, Ray) from PlanetMath have more ideas/technology in this direction.
spitters do you have a link to the PlanetMath version, the thread you gave has dead links.
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