Who Gives a Sheaf? Part 1: A First Example

We take a first look at (pre-)sheaves, as being inspired from first year calculus.

[@kapoioBCS]

Ah yes sheaves, this specific nightmare were first appear in my life in my first algebraic geometry course 😂😂

[@k-theory8604]

Hopefully this mini series will make them less terrifying, lol

[@valentinussofa4135]

Funny comment I've ever seen. 😅

[@rajanalexander4949]

Lucid exposition of a deviously profound concept; looking forward to the subsequent videos; thank you!

[@k-theory8604]

My video output has slowed down a bit, but I'm hoping to return to this series in the Spring!

[@Sqaarg]

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]

I haven't heard of it, I'll be sure to check it out, thanks!

[@aaAa-vq1bd]

yeah it’s wonderful. and it has a bit of interesting philosophical stuff too, although that part is very unfocused.

[@rajanalexander4949]

Thanks for the recommendation

[@fanalysis6734]

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-theory8604]

Thanks! Glad you enjoyed it.

[@RBanerj]

Very clearly explained, great video

[@damonpalovaara4211]

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]

Glad it helped! I'll be making new videos in this series some time this week.

[@themasculinesociety]

I really like your teaching, you made this look easy

[@k-theory8604]

Thanks! Glad you enjoy it!

[@sebastianelytron8450]

I gave enough of a sheaf to watch this video in its entirety, and I'm glad I did.

[@umbraemilitos]

We need more hands on specific examples in higher math.

[@knight3481]

Now do one for etale sheaf.

[@k-theory8604]

Perhaps eventually, but I think it'd be useful to have more videos on basic sheaf theory and schemes first.

[@christopherwithers1131]

nice

[@donnypassary5798]

Haven't got into sheaf part, but I guess it has to do with "binding" presheaves together right?

[@k-theory8604]

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.