ℍᵃⁿⁿᵃʰ 🍀 @ZevenKorian@mathstodon.xyz

it should work right? it's just some sort of quotient space

not sure if this has a name but i¡m trying things like "multi-stalk"

does the definition of stalk of a sheaf work if i consider a finite collection of points rather than a single point?

tbf knowing derivations are basically the same thing as vector fields it's not much of a stretch to imagine how you construct such a coordinate chart

"given a derivation \(D\) non-singular at \(q \in\Omega\) (so like, \(D_q\) is not \(0\)), we can find a coordinate chart for \(\Omega\) around \(q\) such that \(D=\partial_{x_n}\)"

i will take that for granted

also thanks detexify

THAT BEING SAID when I understood what a finite mapping was it also clicked why they are so important relative to coherence

the appendix literally starts out explaining what a presheaf is and basically stays in the comfort zone of the sheafs of analytic functions but still

"I took a lecture into sheaf theory once. Thought it was an interesting construction. Read an appendix on coherent sheaves. Realised my mistake"

why is it a harpoon anyway

why not even a full arrow

why did i even consider category theory to be something fascinating at some point rather than a collection oh hacks

I thought for the longest time it was just the vertical bar you use for restricting a mapping

easy enough when inline but try subscript: \(_\upharpoonright\)

thank god we have digital PDFs nowadays because imagine guessing what \(\upharpoonright\) is

next morning: i no longer process stuff as germs and stalks, but for how long?

that big brain moment when you understand the difference between \(\mathcal{S}(U)\) and \(\mathcal{S}_{\upharpoonright U}\)

2 hours of sheaf theory later: I have a desk lamp on, and my brain just processed it as "a germ of light source"

nothing like actually sitting down and taking notes on an article like you were attending a lecture

i actually UNDERSTOOD stuff this time around

I fear no one

but that thing?

\(\displaystyle\lim_\leftarrow\)

it scares me