following up from a previous tweet, does anybody know of a reference for the fact that the functor Sh:Space^op→Cat is indeed a stack? I only know this as folklore, but am pretty sure it must be written down somewhere!

the fact that both the sentence “sheaves are stacks” and the sentence “sheaves is a stack” not only make grammatical sense and type check, but are also true, has been my source of confusion for the afternoon

S: Should I use "one-to-one" and "onto", or should I use "injective" and "surjective" instead?

Me: Compromise and use "onejective" and "onjective"

S: .... Is this your idea of being helpful?

is there a nice way to redefine `\to` in a LaTeX file so that it becomes `\rightarrow` in inline maths and `\longrightarrow` in display maths?

I had a bunch of researchy tabs open with papers about algebra and stuff and after coming back from lunch I noticed one tab called "Rice fields" and I thought, "Rice fields? Do I know what Rice fields are? Who is Rice? Why was I looking at this?"
It turns out rice fields are fields where rice grows.

what is the algebraic analogue of paracompactness of a manifold? being of finite type? locally Noetherian? some combination with other stuff?

why do we call them "hom-sets" and write Hom(x,y) but then say "morphism" instead of "homomorphism"?

even though i *know* that the pair subdivision of a simplex is cubical, it still blows my mind when you actually *draw* it and end up with something that really looks like an actual cube!

People from Mathstodon: if you want to share your maths with people from other instances, keep in mind that LaTeX rendering is only available on a browser, and for people also on mathstodon.

If you still want to write formulas, mathstodon can be used to export LaTeX to unicode, like \sum to ∑, \prod to ∏, and so on.

Just click on the Tab key and if your equation can be rendered using unicode it will be transformed.

Example: ϕ(x)=∑ₖⁿ xᵏ

It's not perfect, but you can see it on a phone app!

friendly reminder that spectral sequences are sort of just an abstract version of persistent homology, so if you understand one then you can use that intuition to better understand the other!

i don't actually think there'll be any mass exodus fram twitter or that musk will substantially change anything in the short term, i just think mastodon is neat & held back only by the lack of users

announcement (boosts appreciated) 

We're delighted to announce the HoTTEST Summer School, which will take place online everywhere in the world during the months of July and August 2022.

The school will run both synchronously and asynchronously. The lectures will be delivered live (between 2:30-4pm UTC) and paired with various tutorial sessions run by teaching assistants. The course will also feature a discord-based all-hours Q&A and an online archive of all course materials so that participants can follow along on their own schedule.

This school is for everyone and anyone with some familiarity with abstract mathematics or theoretical computer science and an itching to learn about homotopy type theory. Our goal is to make homotopy type theory accessible to, and inclusive of, everyone who is interested, regardless of cultural background, age, ability, formal education, ethnicity, gender identity, or expression. We believe HoTT is for everyone, and are committed to fostering a kind, inclusive environment.

Read more: groups.google.com/g/homotopyty
Join the Discord: discord.gg/tkhJ9zCGs9

I appreciate the posts that people are writing! But I don't like writing my own!! Anyway, I'll try.

I'm a research mathematician, interested in social media for both professional and recreational reasons. If you follow me, you'll see a mix of math and non-math.

Here are four pictures of things I've been involved in. I'll add a little more in a comment below.

A few years ago I made this flow chart of which Mastodon posts end up in which timelines!

So, you can see how each instance will have a different local timeline, and even a slightly different federated timeline - and you can see why the federated timeline moves so much faster than the local one, too.

This is why it's important to boost good posts and use hashtags - the fediverse is fragmented and harder to search by nature.

[ #mastodon #meta #tootorial #howto #mastopedia #mastotip ]

for those new here, here's a tiny guide to what some of the links in the menu are for — note that they're in increasing order of size!

☞ "Home" shows you the activity of the people you follow

☞ "Local" shows you the activity of everybody on this instance (mathstodon.xyz)

☞ "Federated" shows you the activity of everybody on *any* instance that is open for public viewing

Imagine mentioning "symplectic meanders associated to seaweed" to someone, and imagine them believing it is not part of an elaborate joke. This cannot be done.

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