We take a first look at (pre-)sheaves, as being inspired from first year calculus.
Пікірлер: 23
@kapoioBCS Жыл бұрын
Ah yes sheaves, this specific nightmare were first appear in my life in my first algebraic geometry course 😂😂
@k-theory8604 Жыл бұрын
Hopefully this mini series will make them less terrifying, lol
@valentinussofa413511 ай бұрын
Funny comment I've ever seen. 😅
@rajanalexander49495 ай бұрын
Lucid exposition of a deviously profound concept; looking forward to the subsequent videos; thank you!
@k-theory86045 ай бұрын
My video output has slowed down a bit, but I'm hoping to return to this series in the Spring!
@Sqaarg Жыл бұрын
Daniel Rosiak has written a very nice book on sheaves, `Sheaf Theory Through Examples'. It's filled with lots of down to earth examples, and was a joy to read through.
@k-theory8604 Жыл бұрын
I haven't heard of it, I'll be sure to check it out, thanks!
@aaAa-vq1bd Жыл бұрын
yeah it’s wonderful. and it has a bit of interesting philosophical stuff too, although that part is very unfocused.
@rajanalexander49495 ай бұрын
Thanks for the recommendation
@fanalysis67347 ай бұрын
Pretty good video. I especially liked that comment about there being less globally continuous functions and that telling us about the space. Then the picture with differentiation relating to smaller open subintervals is also really insightful
@k-theory86047 ай бұрын
Thanks! Glad you enjoyed it.
@RBanerj6 ай бұрын
Very clearly explained, great video
@damonpalovaara4211 Жыл бұрын
I started reading a book on algebraic analysis and the first chapter was a review of sheaf theory and it used notation that I didn't understand. Thank you for this video, it helped me get through chapter 1
@k-theory8604 Жыл бұрын
Glad it helped! I'll be making new videos in this series some time this week.
@themasculinesociety5 ай бұрын
I really like your teaching, you made this look easy
@k-theory86045 ай бұрын
Thanks! Glad you enjoy it!
@sebastianelytron8450 Жыл бұрын
I gave enough of a sheaf to watch this video in its entirety, and I'm glad I did.
@umbraemilitos11 ай бұрын
We need more hands on specific examples in higher math.
@knight34816 ай бұрын
Now do one for etale sheaf.
@k-theory86046 ай бұрын
Perhaps eventually, but I think it'd be useful to have more videos on basic sheaf theory and schemes first.
@christopherwithers113111 ай бұрын
nice
@donnypassary5798 Жыл бұрын
Haven't got into sheaf part, but I guess it has to do with "binding" presheaves together right?
@k-theory8604 Жыл бұрын
Essentially, although it's a little more "fine-grained" that that. As we'll see in the net video, a sheaf is pre-sheaf that satisfies some extra conditions. Namely, that if you have sections defined on an open cover (so you can think about this as functions defined on open intervals of the real numbers), and they agree on overlaps, then there's a unique section (think function) on the whole space. (In our case the real numbers) So it's not really gluing together pre-sheaves, it's gluing together the sections of the presheaf.