TL;DR: a forum for applied category theory.

Longer version:

LocalCharts is a forum using the software Discourse for the activity of creating local charts of parts of the world and gluing them together.

A forum is a website that provides facilities for users to write posts and then organize them according to category, time posted, and popularity. There are also facilities for other users to comment and vote on/“like” posts. These posts can range from just links to other webpages, to questions, to whole essay-length pieces of prose.

The word chart in the English language refers to a graphical representation of a certain area of land, also known as a map. In mathematics, a local chart is a term in differential geometry, which corresponds to a part of a manifold that is diffeomorphic to \mathbb{R}^n. We use “local chart” in a metaphorical sense to refer to a formalized model of some fragment of reality. For instance, the theory of Newtonian physics is a chart of macro-scale rigid body systems. But we don’t intend to constrain ourselves to what is traditionally known as physics; logic, chemistry, biology, geometry, computer science and many other topics can all equally well be seen as creating charts of fragments of the world.

Finally, gluing them together means finding formal connections between different local charts. The most promising conceptual technology for this that I know of is category theory, which is a mathematical discipline that has achieved astonishing success in the last 70 years in putting different frameworks for doing math and science under a common roof.

More recently, a field of mathematics going under the name “Applied Category Theory” has arisen which uses category theory in a way more directly connected to applications in science and technology than has been the tradition, which typically used category theory in conjunction with fairly abstract math. I hope that LocalCharts can be a useful and productive tool for the Applied Category Theory community, and all others who find appealing the vision of creating and gluing together charts.

General guidelines

This is a forum centered around the pursuit of knowledge. Therefore, the first guideline for how to behave is to ask yourself “am I helping others learn about math and the world?”

But this is also a forum composed of people with feelings. So the second guideline for how to behave is to ask yourself “am I creating a space where others feel comfortable pursuing knowledge; am I being kind?”

And finally, this is a forum where we try to focus and get things done. So the third guideline for how to behave is to ask yourself “am I contributing to what others would identify as the purpose of this forum/category/topic?”

If the answer to all of these questions is yes, then whatever you were going to say is probably suitable for this website.

If the answer to all of these questions is no, then whatever you were going to say is almost certainly not suitable for this website.

If the answers are a mix of yes’s and no’s, then we have a conundrum. There are several ways of solving that conundrum.

0. Ask a moderator. We are here to help!
1. Err on the side of silence. This is safe, but perhaps not optimal.
2. Reword what you were going to say so that the answer to all three questions is yes. This is not always possible.
3. Post elsewhere. If you have a thought in a comment thread on a post that perhaps is not totally relevant, you can write a new post! If you have a concern about whether someone else is behaving appropriately, but you don’t want to publicly shame them, send them a private message. Or post on your personal blog, or make a tweet, or write a zulip message.
4. Post it anyways. This is the “YOLO, better to beg forgiveness” approach, and in this case you should be prepared to face consequences. But if it ends up being received well, you may get away with it.

While this forum is public and open, it is not a “public space” in the sense that your freedom to swing fists only stops at other peoples noses; i.e. “anything goes as long as it doesn’t break explicit rules”. If we do not feel that you are not engaging in the spirit of honest and kind collaboration, you may be asked to leave without us giving a full justification. Dealing with pettiness is a waste of our volunteer moderators time. There’s a whole rest of the internet that you can use to exercise your free speech and we are under no obligation to give you a platform.

Good things to do

These are not rules, but rather tips on how to “seek the good” in forum posting. Violating these will cause people to tell you not to violate them.

• Write clear titles for your posts. 3-8 words is a good length.
• If you are asking a question, see if someone else has already asked that question.
• Complement people. This might sometimes be in conflict with the “don’t derail the conversation”, and “focus on developing math” goals, but writing is hard, and a lot of work, and it can mean a lot to people that others appreciate what they’ve done. If the only comments are things to fix, it can be kind of bleak. Especially for new users who may not be so sure about whether they are contributing, a little positive affirmation can go a long way.
• Keep things tidy; classify your posts well, use headings consistently, proofread, etc.
• Provide proper attribution and citation for other’s work. If you slip up on this one, it’s not a big deal, but repeated, intentional plagarism violates both the guidelines of honesty and kindness.

Concrete things to avoid

Anything in the “unacceptable behavior” section of the Citizen Code of Conduct.

Anything a moderator has told you not to do.

Tips and tricks

Quiver

You can use quiver by copying the embed code and then pasting it into your post, like the following

When editing your post, quiver constantly refreshes on every edit, so you can comment it out with <!-- quiver embed --> until you are done editing.

Collaborative editing

You can use docs.localcharts.org to write posts collaboratively in markdown, and then copy-paste them into the editor here. (TODO: set this up)

RSS

Almost any page on discourse can be turned into an RSS feed by adding .rss to the end of the URL.

Full-screen mode

You can go into full-screen mode while editing a post by clicking on the arrows in the top right corner of the edit box.

In my mind, LocalCharts serves three purposes.

1. Aggregation. I think a public place where links to new blog posts in the category theory world are posted would do the community a service in making people’s work in blog posts more visible.

   One feature of LocalCharts is that it will automatically post links from various category theory blog RSS feeds (only with the consent of the authors of those feeds), so that you can keep up to date with a wide variety of blogs just by going to LocalCharts.

2. Informal, longform content. The happy medium between “write a tweet/zulip post” and “write a nlab article/paper” is “write a blog.” But I think that for most people, it’s quite hard to get the volume of blog posts necessary for a personal blogging site to get much traction. It’s hard to stay motivated to write blog posts when you aren’t sure if anyone is even reading them. LocalCharts should hopefully provide the community feedback that will motivate informal, longform content.

3. Long-term knowledge storage. Tweets and zulip posts are very ephemeral. A forum thread, on the other hand, is searchable and linkable, and you can bookmark/share/cite it.

Comparison with other platforms

arXiv

Sometimes you want to write things up before they have developed enough to be a full paper, so that you can ask questions about things. Also, sometimes you want to write in a much more informal style. And you want to get feedback immediately, rather than waiting 4 months for a reviewer to get back to you.

On the other hand, writing things up in full detail as a paper is sometime a very good thing to do. I hope that when you do that, and post it to arXiv, you will then post a link in LocalCharts and a short description of the paper so that other people know to read it!

nLab

Writing for the nLab has an expectation that you are writing up the “canonical” definition of things, from the nPOV. This is very good for an encyclopedia, but there’s plenty of good content that can be written that’s not in the nPOV. If you want to explain a topic to someone, the best way to do it is not via a web of tersely written encyclopedia entries; you want to put a narrative spin on a sequence of topics.

Additionally, I envision a slightly different focus for LocalCharts as being more focused on applied category theory than higher category theory.

That being said, I hope that the eventual result of a good LocalCharts discussion is new entries in the nLab!

nForum

The nForum is a good place to talk about the nLab. However, I envision LocalCharts as having a distinct focus from the nForum. For one, LocalCharts will be more of a “link aggregator” for content across the internet, not just ncatlab. Additionally, LocalCharts will be a place to write content, not just a place to discuss content written elsewhere.

Category Theory Zulip

I love zulip and use it daily. Here are the things I love about zulip.

• Great UI; looks much better than slack in my opinion
• Threading: makes it possible to have multiple conversations in a channel
• It’s a good “directory” for category theory; I can reliably DM people
• I like having conversations on Zulip, especially being able to chat with LaTeX!

However, for me the most productive use of zulip happens in closed channels with <20 people. The volume of chat that happens in the general channels is too much for me to keep up with, and the fact that zulip is constantly showing me all of the chats I haven’t read yet stresses me out.

Additionally, although there isn’t technically a word limit (or at least, not one that I’ve hit) on zulip posts, the UI encourages them to be small. Moreover, zulip threads load from the bottom; when you click on a thread you see the most recent posts first. Thus, zulip encourages conversations, not really content. I would never “write something up” in a zulip post; people might respond to it, but it would quickly get lost! Finally, zulip is not linkable, so I can’t share around things that I’ve written on zulip.

That being said, there is integration between Discourse and zulip, and I plan to set it up so that every time there is a new post on LocalCharts, there is automatically a post on zulip that links to it. This way, if you are a zulip regular you don’t have to check LocalCharts frequently in order to stay up to date.

The n-Category Cafe

The n-Category Cafe is a really great site, but only a couple people can write on it, so it clearly cannot serve the kind of role that I’m hoping for LocalCharts.

That being said, I hope that the n-Category Cafe authors will continue to write there, and I hope that LocalCharts will drive more traffic to the n-Category Cafe.

Category Theory Twitter

I’m kind of addicted to twitter these days. Honestly, one of my hopes for LocalCharts is that it will allow me to get my fix for social interaction with the category theory community without going to twitter.

I think that there are a lot of dark patterns in twitter that keep me and others going back to it, but even if you try to avoid those, currently it’s one of the best places to go to get exposure, and it’s a lot of fun. But I think a lot of the time spent on twitter is wasted. Furthermore, I think that although I have seen productive math conversations on twitter, they are few and far between because it’s hard to have a good conversation when you don’t have LaTeX and you have to squeeze your thoughts into 140 characters (or however long it is now).

I might try to get a twitter bot that reposts LocalCharts posts on twitter though, and I am certainly going to use twitter a lot to promote LocalCharts.

Why Discourse?

I’ve actually thought a lot about this. My original idea for this forum was to use ForumMagnum, which is the software that LessWrong runs on. While ForumMagnum has a variety of very nice features, my eventual conclusion was that the technical side of ForumMagnum was too customized for lesswrong/effective altruism forum/alignment forum for it to be practical for me to port it on my own.

I also evaluated a large number of other wiki softwares and other link aggregators/reddit clones. My conclusion was that none provided as complete of a package as Discourse. It seems in some ways that Discourse has simply won the forum wars for the time being, and many of the open source communities that I follow use Discourse. I believe that this community will succeed or fail more on the people involved than on the technology, so it seemed sensible to just pick a “safe default” and then go from there. Discourse is made by what seems to be a well-funded company, is relied on by many, many organizations, and is built on a tried-and-tested technology stack.

Discourse boasts a large number of integrations with other platforms, specifically RSS and Zulip, and hopefully in the future it should integrate with the fediverse, i.e. Mastodon and other ActivityPub implementations. Additionally, there is a wide variety of plugins and features for Discourse that I have yet to explore; hopefully needs of this community that come up unexpectedly in the future will be addressed by them!

I do have some complaints with Discourse; I would prefer nested replies to a single reply stream because I want this to be a contrast to zulip. But I overall hope that Discourse will end up being a reasonable compromise that will get the job done.

Right now, me! (Owen Lynch). Additional moderators include: @KevinDCarlson.

Kevin and I are employees of the Topos Institute, which is a nonprofit centered around applied category theory, but the Topos Institute currently has no formal connection with LocalCharts, and is not legally responsible for anything on this site.

You can send feedback by sending any of our admins a DM, who are currently

• @owenlynch

or by emailing owen@topos.institute.