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I would like to ask the opinion of the community and (especially) the nLab steering committee about applied category theory content on the nLab. For those who don’t know about applied category theory, we are about to hold our second conference next week, so you can get some idea about people and topics from the list of accepted papers.
There are either two or three options:
Applied category theory content is simply added to the nLab
There is a separate sub-wiki such as ncatlab.org/act/ that functions like a personal subdomain but is publically editable
There is a totally separate “rival” wiki
I would like to ask the specific question of whether the middle option is possible in principle, or whether it wouldn’t be allowed. (I would certainly understand if the steering committee won’t allow it!)
I know that many applied category theorists claim to prefer the first option (and I imagine that most nLabers would go for the first option as well), but in practice there has been almost no contribution so far. (This is, of course, on me as much as anybody else.) Here I will lay out my personal reasons for preferring options 2 or 3, and I would appreciate feedback on specific points.
Applied category theory does not usually align well with the n-pov. (Personally I explicitly reject the n-pov and would set a contrasting policy of “use the right amount of abstraction for your problem domain, but no more”.) I note that the application domains that are already well-represented on the nLab, such as type theory and parts of theoretical physics (I believe this is an exhaustive list), are precisely those that align well with the n-pov.
The nLab has a built-in preference for certain fields, namely mathematics, physics and philosophy. Many applied category theorists are working towards other fields, such as computer science, statistics, chemistry, biology, engineering, economics, finance, linguistics, etc. I believe the nLab’s explicit preference for physics will make these fields feel like “second class citizens”.
I would like to see (and write) pages purely about a domain area, setting out the important ideas and the problems that “users” would like to solve. In some cases that may involve no category theory whatsoever. I believe this would be off-topic on the nLab and might risk deletion, without a policy change.
Although it isn’t inherent to the field, many applied category theorists would prefer more pedagogical articles compared to the nLab’s famously (infamously) heavy style. I think a separate wiki would be able to serve a dual purpose as a “1catlab” analogous to simple.wikipedia.org. Of course, there is also a lot to be said for adding pedagogical material to the nLab.
Related to the previous point, many young researchers have a lot of contribute about their problem domain but are intimidated by the nLab’s style, especially when it comes to contributing content that may not even be on-topic.
Experience shows that the cold start grand plans rarely materialize to their promise. Accordingly, before a sub-web is created, we ask that the respective author(s) first show some activity on the main web.
If you have something to add, just go ahead, create an entry in the main web and add material. The practical editing will help to get an idea for how much energy it takes to add a non-trivial amount of content. If, after a while. it really turns out that there is so much new content and indeed so alien to the core Lab that it needs to be moved into a separate web, if that indeed happens, then it’s still easy enough to move.
This sounds very reasonable. The only downside I can see is that it might be hard to see how much work has gone in. (But on the plus side, it will give me an idea how much work must go into leading such a project, i.e. a lot.)
Just a few thoughts about your bullet points:
I don’t see any conflict between “use the right amount of abstraction for your problem domain, but no more” and the nPOV. The “general usefulness” of category theory as laid out in the nPOV doesn’t mean that it solves every problem, or that more abstraction is always better. If the page nPOV gives these impressions, then we should edit it.
Very interesting point! I actually can’t see any reason offhand for the nLab to privilege physics and philosophy over other fields that use mathematics. Would anyone object to changing the slogan to something more encompassing like “mathematics and its applications”?
There are plenty of pages on the nLab that involve no or very little category theory (yet). So no, I don’t think such pages would be off-topic at all. As long as you are not averse to someone else adding some category theory (or anything else, really – the site being a wiki) later on if they feel like it.
The nLab’s “heavy style” is not a house mandate. In fact, many regulars (maybe even all of us) don’t like it! Please, please, give us your expository writing! Spread the word to your students!
Also, just a point of experience: we recently tried something like your second-option with the homotopy type theory web. It hasn’t been a total failure, but I’d say pretty close. I’m close to recommending that we close it down and merge whatever information and energy is there back into the main nLab.
Here’s an analogy that just occurred to me. I was talking to someone today about how proof assistant code that goes along with a book can be archived by the publisher, and I argued that it’s often better to incorporate the code into a library that is under active development and maintenance. If all the publisher does is save the code as it existed at publication date, then probably within a few years it won’t even compile any more with the current version of the software, and within a decade or two the version of the software that it did run on may not even be available to install. Similarly, writing that’s contributed to the main nLab will continue to be edited, maintained, updated as the software changes, interlinked with other articles, etc. even after whoever wrote it has moved on to other things.
The “mathematics, physics and philosophy” tag came from the n-Café reflecting the original interests of John, Urs and myself. But there is no such limitation here. We have entries such as blockchain, monads (in linguistics) and, one for you, lens (in computer science). Not to say that they’re well-developed, but whatever we have is just due to the energy and interests of contributors.
Yeah, having it all in the main web is the best.
Don’t think in boxes, let your mind roam freely.
Ok, then I will focus my effort on the main web and everybody can see how it goes. Thanks for feedback!
I’m late to this, but re the infamous heavy style: my own inclination is to try to write for a level appropriate to a beginning graduate student in category theory, if possible.
It is, however, important not to disparage the efforts of people whose problem domains require more abstraction than yours does, and to be open to the occasional suggestion that your problem domain might benefit from more abstraction than you’re aware of.
Also, to all potential newbies: Don’t get hung up on all these meta thoughts. Focus on bringing in your maths content, and leave worries about other points of view for later or to others.
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