Basic Category Theory by Tom Leinster | Free Ebook Download

Bookmarked Basic Category Theory (arxiv.org)
This short introduction to category theory is for readers with relatively little mathematical background. At its heart is the concept of a universal property, important throughout mathematics. After a chapter introducing the basic definitions, separate chapters present three ways of expressing universal properties: via adjoint functors, representable functors, and limits. A final chapter ties the three together. For each new categorical concept, a generous supply of examples is provided, taken from different parts of mathematics. At points where the leap in abstraction is particularly great (such as the Yoneda lemma), the reader will find careful and extensive explanations.
Tom Leinster has released a digital e-book copy of his textbook Basic Category Theory on arXiv [1]

h/t to John Carlos Baez for the notice:

My friend Tom Leinster has written a great introduction to that wonderful branch of math called category theory! It’s free:

https://arxiv.org/abs/1612.09375

It starts with the basics and it leads up to a trio of related concepts, which are all ways of talking about universal properties.

Huh? What’s a ‘universal property’?

In category theory, we try to describe things by saying what they do, not what they’re made of. The reason is that you can often make things out of different ingredients that still do the same thing! And then, even though they will not be strictly the same, they will be isomorphic: the same in what they do.

A universal property amounts to a precise description of what an object does.

Universal properties show up in three closely connected ways in category theory, and Tom’s book explains these in detail:

through representable functors (which are how you actually hand someone a universal property),

through limits (which are ways of building a new object out of a bunch of old ones),

through adjoint functors (which give ways to ‘freely’ build an object in one category starting from an object in another).

If you want to see this vague wordy mush here transformed into precise, crystalline beauty, read Tom’s book! It’s not easy to learn this stuff – but it’s good for your brain. It literally rewires your neurons.

Here’s what he wrote, over on the category theory mailing list:

…………………………………………………………………..

Dear all,

My introductory textbook “Basic Category Theory” was published by Cambridge University Press in 2014. By arrangement with them, it’s now also free online:

https://arxiv.org/abs/1612.09375

It’s also freely editable, under a Creative Commons licence. For instance, if you want to teach a class from it but some of the examples aren’t suitable, you can delete them or add your own. Or if you don’t like the notation (and when have two category theorists ever agreed on that?), you can easily change the Latex macros. Just go the arXiv, download, and edit to your heart’s content.

There are lots of good introductions to category theory out there. The particular features of this one are:
• It’s short.
• It doesn’t assume much.
• It sticks to the basics.

 

References

[1]
T. Leinster, Basic Category Theory, 1st ed. Cambridge University Press, 2014.

GoodReads 2017 Reading Challenge: 42 Books

I want to read at least 42 books this year.

I totally fell down on the job last year (compared to my goal), but I did read a lot of additional material online instead and lot of what I did read, (but didn’t necessarily finish toward my goal) was of a highly dense/technical nature. We’ll do better this year.

Reply to Ben Hanowell about Hypothes.is, Fragmentions, and Annotations

Replied to a tweet by Brash EquilibriumBrash Equilibrium (Twitter)
@ChrisAldrich is this the fragmentions plugin along with @hypothes_is or just the latter? Link to instructions por favor!!!!
Hypothes.is’ reply will get you most of the way, but I’ll add some additional thoughts below.

There are a couple of fragmentions plugins in the WordPress repository. I use and recommend WP Fragmention. Mostly it comes down to supporting a chunk of javascript that is the brainchild of Kevin Marks.

For Hypothes.is, I use the plugin referenced in the tweet above, but I’ve also been using Hypothes.is Aggregator by Kris Shaffer. I will note that the latter broke for me recently (possibly with the upgrade to WP 4.7, but I’ve filed a ticket and hopefully it’ll get sorted shortly). Shaffer’s plugin also makes using and posting with Hypothes.is’ Chrome extension more useful and interesting to me, since I can own copies of my highlights/annotations on my own website.

I’m hoping that sometime soon that Hypothes.is highlights and annotations on pages will also support sending webmentions so that when someone annotates one of my pages that I’ll receive a notification about it, almost as if it were a comment. If you’re interested in this sort of thing, Kartik Prabhu has a fantastic write up and some code on mixing marginalia and webmentions which I’m hoping to implement sometime soon myself.

If you need any help with any of the above, I (and surely others) are happy to help you via IndieWeb Chat.

A Secondary Meaning for POSSE

I’d meant to document this back in November when it was discussed at IndieWebCamp Los Angeles, but it was a busy weekend.

In conversation with Tantek Çelik, I asked if a double entendre meaning to POSSE was originally intended when it was coined?

POSSE is an abbreviation for Publish (on your) Own Site, Syndicate Elsewhere (or Everywhere), a content publishing model that starts with posting content on your own domain first, then syndicating out copies to 3rd party services with permashortlinks back to the original on your site.

When I originally heard about POSSE, I considered the original post on my own site as the Sheriff or “leader” and the ensuing syndicated copies as the (literal and figurative) traditional posse which follows along behind it adding ideas, conversation, and help in accomplishing the original post’s mission.

The posse, one tough looking gang of o’n’ry corporate silos! Let’s mount ’em up!

If that second meaning didn’t exist before, it does now…

totes profesh: how to blog about code and give zero fucks

Read totes profesh: how to blog about code and give zero fucks by Garann Means (garann.com)

I'm frustrated right now. I've been looking for someone to write about a technology that tons of people have no doubt used and am coming up short. Really, this is my own fault, because I was hoping I'd find someone who wasn't a white male to address the topic. There's nothing wrong with a white male addressing the topic, but I've been recommending a lot of white males to write about technologies and I was hoping to put my money where my mouth is in terms of my hopes for the diversity of the field in which I work.

I checked a bunch of related repos on GitHub and found that the maintainers were white guys and the committers were white guys and the people filing issues were white guys. So I checked the Following lists of related Twitter accounts and found.. more white guys. The few women I found either didn't blog or had Tumblrs full of inspirational quotes and cupcake photos and shit. (Which is fine. But not what I happened to be looking for an expert on.)

And so this is how I became frustrated, because I don't want to hit up people I know over and over again, and I need a way to know people are interested in and knowledgeable about certain topics, and the internet was giving me fuck-all.

Which brings me to the subject of this post, which is that you, developer in an underrepresented group who hopefully received this link somehow through the magical machinations of social media, should be blogging more. I need you to blog more. Little future developers who look or act or dress or think like you need you to blog more. Your slightly confused and defensive developer community needs you to blog more. Please please please please. And if you are like, "I give zero fucks about what those people need, I need to get off work at six and build charming birdhouses or customize my bicycle or something," the best part is giving zero fucks is totally fine.

See, if you were an ambitious type, you wouldn't need me to prevail upon you to blog more. You would be doing that and speaking at conferences and merrily on your way to becoming the next Marissa Mayer and that would be just fine for everyone. But there are a lot more not-Marissa-Mayers in the world than there are Marissa Mayers and those people need representation, lest we get it into our obsessive little developer heads that if you are not constantly being the very best at everything you should just go home. We need blog posts that aren't about big fluffy TED topics like programmer diversity and are instead about that fucking stubborn and reprehensible bug you spent five hours on today because you couldn't find a goddamned thing on StackOverflow.

📺 "Blue Bloods" Genetics

Watched "Blue Bloods" Genetics S7 | E11 from CBS, January 6, 2017
Directed by Alex Chapple. With Donnie Wahlberg, Bridget Moynahan, Will Estes, Len Cariou. When Eddie and Jamie become overly involved in a complicated adoption case between the birth and adoptive parents, they ask Erin to help them settle the dispute without going to court. Also, Frank looks into reports of NYPD cadets cheating on their psychological exams, and Danny learns that Jack plans to enlist in the Marines after graduation.
Biological parents come back 5 years later to try to get their adopted son back?!

📺 Watched Varsity Blues

Watched Varsity Blues from Paramount, January 15, 1999
Directed by Brian Robbins. With James Van Der Beek, Jon Voight, Paul Walker, Ron Lester. A back-up quarterback is chosen to lead a Texas football team to victory after the star quarterback is injured.
One of those times that I get wrapped up in a cheeseball movie just because it happens to be on cable.

📺 Watched "America’s Next Top Model" Make Your Mark S23 | E3

Watched "America's Next Top Model" Make Your Mark S23 | E3 from VH1, December 23, 2016
With Rita Ora, Ashley Graham, Law Roach, Drew Elliott.
I remember watching this in season 1 and 2. It’s definitely different, still stupidly addictive, but it’s also not as sharp as it used to be production wise. The primary difference seems to be the host has changed and the tagline has gone from “fierce” to “boss”.

📺 Watched "America’s Next Top Model" Major Key Alert S23 | E4

Watched "America's Next Top Model" Major Key Alert S23 | E4 from VH1, January 2, 2017
With Rita Ora, Ashley Graham, Law Roach, Drew Elliott.
Suckered into a second episode because it autoplayed after the last one. Not engaging enough to watch more than this one last episode. Unless something goes awfully awry, I could easily guess who the final contestants will be.

📺 Watched "The Late Show with Stephen Colbert" Charlie Rose/Hayden Panettiere/Jack Maxwell S2 | E72

Watched "The Late Show with Stephen Colbert" S2 | E72 from imdb.com
With Stephen Colbert. TV host Charlie Rose (Charlie Rose (1991) and CBS This Morning (2012)); actress Hayden Panettiere (Nashville (2012)); TV personality Jack Maxwell.
Awesome segment with Charlie Rose. The Charlie Rose in a Can bit was particularly funny.

https://www.youtube.com/watch?v=zKp1OvR197A

Break the logjam with a simple API

Read Break the logjam with a simple API by Dave Winer (Scripting News)

It just takes one storage service to decide to bridge the gap and a wonderful era of innovation can begin.

Background

Some people assume that for a user to be independent of silos, they would need to run a server. This is not true. With a tiny connection between JavaScript running in the browser and a cloud-based storage service, we can do anything a server can do without the server, entirely in the browser.

This isn't a question. In 2016, the technology is mature, we know how it works.

How to

Here's a sketch of how the service would work.

  1. Start with a user-facing service like Dropbox, Google Drive, Amazon Cloud Drive.
  2. Add an API that allows a JavaScript app running in the browser to write into a folder in a user's space. The user grants access via oAuth, as they do with Twitter, Facebook, etc.
  3. Connect to a registrar to allow a user to associate a domain name with a folder. Or map a domain they register elsewhere. A revenue opportunity.

That's it. Now I can hook my JS-in-the-browser app to your service. The user manages it through the UI you already support. And we've opened up a new area for developers to be creative. And most important, it says the exploration of great writing tools can advance outside of Medium. (That's how important Medium has been for the last few years.)

BTW, for Amazon, they would use the S3 API, which is supported everywhere. The apps would pop up very quickly for their service.

It's a total logjam and could be broken by one storage service deciding to help the users break free of silos.

Reply to Dave Rupert’s Poll with another alternative

Replied to a tweet by Dave RupertDave Rupert (Twitter)
Anyone else starting to look for a way out of Twitter?
#4 IndieWeb: Publish on your own site, syndicate elsewhere. (The missing option.)

I’ve been microblogging from my own site and syndicating content to Twitter and other social silos for a while.

I usually consume Twitter via an RSS hack and respond either via Woodwind.xyz which micropubs directly to my site or from a built in RSS reader on my own site. I use Brid.gy and webmention to collect replies back to my site to continue the conversation.

For me, my personal website is my end-all-be-all hub for reading/publishing and Twitter, Facebook, et al. are just distribution channels.

From what I understand about Manton’s proposed implementation, he’ll be using or making a lot of these technologies available, he’ll just be making it a bit easier for my parents and the “masses” to do it.

Reply to Antonio Sánchez-Padial about webmentions for academic research

Replied to a tweet by Antonio Sánchez-PadialAntonio Sánchez-Padial (Twitter)
Hi there @ChrisAldrich! I'd like to add webmentions, but I haven't worked on it yet. What kind of collaboration are you thinking about?
Many academics are using academic related social platforms (silos) like Mendeley, Academia.edu, Research Gate and many others to collaborate, share data, and publish their work. (And should they really be trusting that data to those outside corporations?)

A few particular examples: I follow physicist John Carlos Baez and mathematician Terry Tao who both have one or more academic blogs for various topics which they POSSE work to several social silos including Google+ and Twitter. While they get some high quality response to posts natively, some of their conversations are forked/fragmented to those other silos. It would be far more useful if they were using webementions (and Brid.gy) so that all of that conversation was being aggregated to their original posts. If they supported webmentions directly, I suspect that some of their collaborators would post their responses on their own sites and send them after publication as comments. (This also helps to protect primacy and the integrity of the original responses as the receiving site could moderate them out of existence, delete them outright, or even modify them!)

While it’s pretty common for researchers to self-publish (sometimes known as academic samizdat) their work on their own site and then cross-publish to a pre-print server (like arXiv.org), prior to publishing in a (preferrably) major journal. There’s really no reason they shouldn’t just use their own personal websites, or online research journals like yours, to publish their work and then use that to collect direct comments, responses, and replies to it. Except possibly where research requires hosting uber-massive data sets which may be bandwidth limiting (or highly expensive) at the moment, there’s no reason why researchers shouldn’t self-host (and thereby own) all of their work.

Instead of publishing to major journals, which are all generally moving to an online subscription/readership model anyway, they might publish to topic specific hubs (akin to pre-print servers or major publishers’ websites). This could be done in much the same way many Indieweb users publish articles/links to IndieWeb News: they publish the piece on their own site and then syndicate it to the hub by webmention using the hub’s endpoint. The hub becomes a central repository of the link to the original as well as making it easier to subscribe to updates via email, RSS, or other means for hundreds or even thousands of researchers in the given area. Additional functionality could be built into these to support popularity measures as well to help filter some of the content on a weekly or monthly basis, which is essentially what many publishers are doing now.

In the end, citation metrics could be measured directly on the author’s original page by the number of incoming webmetions they’ve received on it as others referencing them would be linking to them and therefore sending webmentions. (PLOS|One does something kind of like this by showing related tweets which mention particular papers now: here’s an example.)

Naturally there is some fragility in some of this and protective archive measures should be taken to preserve sites beyond the authors lives, but much of this could be done by institutional repositories like University libraries which do much of this type of work already.

I’ve been meaning to write up a much longer post about how to use some of these types of technologies to completely revamp academic publishing, perhaps I should finish doing that soon? Hopefully the above will give you a little bit of an idea of what could be done.