Hi John. It’s great that you’re doing this course, and that registration figure is impressive!

However… there is something near the very start of your course that I really strenuously disagree with. You’ve already heard some version of what I’m about to say, because I said it to everyone at the Applied Category Theory meeting we both attended in Leiden. But at the time I didn’t realize we differed on this.

Here it is. Lecture 2, “What is Applied Category Theory?”, begins with the words

“Applied category theory” is fairly new.

and then a bit later you say that the term “applied category theory”

also mainly means applications outside computer science.

*You* might mean it that way, but *I* don’t, and I think the usage you’re encouraging is an awful mistake.

It also seems unnecessarily rude to those who apply category theory to computer science. That’s a set of applications at least as deserving of the term as any other. And as you mention, applications of category theory to computer science have been important for decades. That stuff *is* applied category theory in any reasonable sense of the phrase, and it’s *not* new. And honestly, if that was my research area — which it’s not — then I’d be pretty pissed off to hear someone influential saying that applied category theory was new, or that the applications of category theory I work on don’t count.

(I know you have abundant respect for the applications of category theory to computer science, because I know you personally. But I think your restrictive usage of the term “applied category theory” could easily be construed as disrespectful, even though you surely don’t intend it to be.)

Let’s step back and think about the more general term “applied mathematics”. For historical reasons, most mathematicians’ default interpretation of “applied mathematics” is much narrower than it could be. It’s usually understood to mean something like “methods of analysis applied to physical problems”. Someone who studies the Navier–Stokes equations will typically be called an applied mathematician, even if they’ve never touched a fluid in their research life. But someone who applies number theory to cryptographic systems, or knot theory to problems of genetic recombination, or category theory to the design of programming languages, will usually not be. Whether someone is called an “applied mathematician”, or is said to do “applied mathematics”, has little to do with their proximity to any actual application. It’s just a product of how language and culture have evolved.

I hope mathematicians and other scientists hurry up and realize that there’s a glittering array of applications of mathematics in which non-traditional areas of mathematics are applied to non-traditional problems. It does no one any favours to keep using the term “applied mathematics” in its current overly narrow sense. People coming up with exciting and unconventional applications of mathematics (including exactly the kinds of things you’re lecturing about) fully deserve the credit for doing applied mathematics. We should fight for the term “applied mathematics” to be used in the broadest and most inclusive way possible.

For much the same reasons, I’m dismayed (and actually a bit shocked) to see you declaring that applied category theory “mainly means applications outside computer science”. Why exclude them? It doesn’t make sense as a use of language, it’s potentially insulting, and it gives a false impression. After all, when we’re talking about applications of category theory outside mathematics, applications to computer science are the most conspicuous success story of all.

Of course, you and others are free to use “applied category theory” to mean anything you want, and if for some reason you want to exclude computer science, you can. But that would be like me declaring:

“Californians” mainly means people from California who aren’t called John.

We get to decide how to use language. You’re giving a course to hundreds of people; you’ll have an influence on how the term “applied category theory” comes to be used. Why would you want to exclude applications to one particular field? Obviously you can exclude applications to computer science from your *lectures* — that’s not the issue — but why would you want to exclude them from the term “applied category theory” itself?

## Re: Applied Category Theory: Ordered Sets

Hi John. It’s great that you’re doing this course, and that registration figure is impressive!

However… there is something near the very start of your course that I really strenuously disagree with. You’ve already heard some version of what I’m about to say, because I said it to everyone at the Applied Category Theory meeting we both attended in Leiden. But at the time I didn’t realize we differed on this.

Here it is. Lecture 2, “What is Applied Category Theory?”, begins with the words

and then a bit later you say that the term “applied category theory”

Youmight mean it that way, butIdon’t, and I think the usage you’re encouraging is an awful mistake.It also seems unnecessarily rude to those who apply category theory to computer science. That’s a set of applications at least as deserving of the term as any other. And as you mention, applications of category theory to computer science have been important for decades. That stuff

isapplied category theory in any reasonable sense of the phrase, and it’snotnew. And honestly, if that was my research area — which it’s not — then I’d be pretty pissed off to hear someone influential saying that applied category theory was new, or that the applications of category theory I work on don’t count.(I know you have abundant respect for the applications of category theory to computer science, because I know you personally. But I think your restrictive usage of the term “applied category theory” could easily be construed as disrespectful, even though you surely don’t intend it to be.)

Let’s step back and think about the more general term “applied mathematics”. For historical reasons, most mathematicians’ default interpretation of “applied mathematics” is much narrower than it could be. It’s usually understood to mean something like “methods of analysis applied to physical problems”. Someone who studies the Navier–Stokes equations will typically be called an applied mathematician, even if they’ve never touched a fluid in their research life. But someone who applies number theory to cryptographic systems, or knot theory to problems of genetic recombination, or category theory to the design of programming languages, will usually not be. Whether someone is called an “applied mathematician”, or is said to do “applied mathematics”, has little to do with their proximity to any actual application. It’s just a product of how language and culture have evolved.

I hope mathematicians and other scientists hurry up and realize that there’s a glittering array of applications of mathematics in which non-traditional areas of mathematics are applied to non-traditional problems. It does no one any favours to keep using the term “applied mathematics” in its current overly narrow sense. People coming up with exciting and unconventional applications of mathematics (including exactly the kinds of things you’re lecturing about) fully deserve the credit for doing applied mathematics. We should fight for the term “applied mathematics” to be used in the broadest and most inclusive way possible.

For much the same reasons, I’m dismayed (and actually a bit shocked) to see you declaring that applied category theory “mainly means applications outside computer science”. Why exclude them? It doesn’t make sense as a use of language, it’s potentially insulting, and it gives a false impression. After all, when we’re talking about applications of category theory outside mathematics, applications to computer science are the most conspicuous success story of all.

Of course, you and others are free to use “applied category theory” to mean anything you want, and if for some reason you want to exclude computer science, you can. But that would be like me declaring:

We get to decide how to use language. You’re giving a course to hundreds of people; you’ll have an influence on how the term “applied category theory” comes to be used. Why would you want to exclude applications to one particular field? Obviously you can exclude applications to computer science from your

lectures— that’s not the issue — but why would you want to exclude them from the term “applied category theory” itself?