Recently I've been working on a dissertation proposal, which is sort of like a culmination of five years of graduate school (yay). The first draft was rough, but I sent it to my advisor anyway. A few days later I walked into his office, smiled, and said hello. He responded with a look of regret.

Advisor: I've been... remiss about your proposal.

[Remiss? Oh no. I can't remember what the word means, but it sounds really bad. The solemn tone must be a context clue. My heart sinks. I feel so embarrassed, so mortified. He's been remiss at me for days! Probably years! I think back to all the times I should've worked harder, all the exercises I never did. I knew This Day Would Come. I fight back the lump in my throat.]

Me: Oh no... oh no. I'm sorry. I shouldn't have sent it. It wasn't ready. Oh no....

Advisor: What?

Me: Hold on. What does remiss mean?

Advisor [confused, Googles remiss]: I think I just mean I haven't read your proposal.

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Announcing Applied Category Theory 2019

Hi everyone. Here's a quick announcement: the Applied Category Theory 2019 school is now accepting applications! As you may know, I participated in ACT2018, had a great time, and later wrote a mini-book based on it. This year, it's happening again with new math and new people! As before, it consists of a five-month long, online school that culminates in a week long conference (July 15-19) and a week long research workshop (July 22-26, described below). Last year we met at the Lorentz Center in the Netherlands; this year it'll be at Oxford.

Daniel Cicala and Jules Hedges are organizing the ACT2019 school, and they've spelled out all the details in the official announcement, which I've copied-and-pasted it below. Read on for more! And please feel free to spread the word. Do it quickly, though. The deadline is soon!


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Limits and Colimits Part 3 (Examples)

Once upon a time, we embarked on a mini-series about limits and colimits in category theory. Part 1 was a non-technical introduction that highlighted two ways mathematicians often make new mathematical objects from existing ones: by taking a subcollection of things, or by gluing things together. The first route leads to a construction called a limit, the second to a construction called a colimit.

The formal definitions of limits and colimits were given in Part 2. There we noted that one speaks of "the (co)limit of [something]." As we've seen previously, that "something" is a diagram—a functor from an indexing category to your category of interest. Moreover, the shape of that indexing category determines the name of the (co)limit: product, coproduct, pullback, pushout, etc.

In today's post, I'd like to solidify these ideas by sharing some examples of limits. Next time we'll look at examples of colimits. What's nice is that all of these examples are likely familiar to you—you've seen (co)limits many times before, perhaps without knowing it! The newness is in viewing them through a categorical lens. 

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