seeing more math on the TL recently. i haven't mathposted in a long time but i'm still happy to field math questions from twitter peeps, just reply here or tag me or w/e. big meaty philosophical questions like "wtf are real numbers anyway" would be particularly fun for me rn
Conversation
eli5 sheaf
1
2
Replying to
5-year-olds do not need to know what sheaves are 😅 imo if you really want to get a handle on this better to dive into the history - why did anyone invent sheaves, what problems were they trying to solve. good place to start is differential equations
e.g. there's a sheaf of solutions to the differential equation df / dz = 1 / z in the complex plane minus a point (namely, branches of the logarithm). this sheaf has no global sections, meaning there isn't a globally defined solution, but there are local ones
1
2
sheaves are the thing you invent trying to understand this "local vs. global" sort of stuff. this particular sheaf happens to be locally constant which is very nice b/c that means it can be described as a representation of the fundamental group, gets into that fun alg top
2