23-JUN-2026

0940

I had been working off the 2017 draft, which I think I probably grabbed in 2017 and just never came around to work on until recently. I ordered a print copy. Color me surprised when I saw the numbering misaligned. This means ‘sane-up-to-1.2.’ above should’ve been ‘sane-up-to-1.1.’ which it still is but I misnamed it. :)

I renumbered everything and finished out up to 1.1.B, this required a lengthy sidequest to upgrade atlas to better encode the approach here. When formalizing text, authors like to pack like-results together and my approach in GIYF was not scaling well with this. Theorems felt separate even when they were the same item in the book, names were getting complicated, big pain.

Atlas v2 has a very different structural UI then the version currently used by GIYF, so another ‘big giant refactor’ will be coming soon I suspect.

High Tide started as a way to get enough context on something I stumbled on while thinking about GIYF’s Line structure. I think what I found is what Vakil describes in chapter 15, “Line Bundles” – I do not speak enough of the language to be sure of this, but my idea is roughly matching the description of a ‘Sheaf of Bounded Tanglings’ in my parlance, and just based on the names I suspect my ‘Tangling’ corresponds to the ‘set of base points’ or ‘base locus’ of L, the idea is that the lines in the sheaf are the global sections?

I have truly no idea if any of what I just said is correct, but that’s why I’m in the book, it’s a race to Chapter 15 to understand if this is the structure I spotted or if I was looking at something else.

To that end, my plan so far is basically to sprint from Chapter 1 to Chapter 15; with the early chapters receiving a pretty thorough treatment, and growing more sparse as I get closer to the target chapters, then probably a pretty thorough work through of Line Bundles. My hope is mostly to gain some technical skill around working with categories/sheaves/schemes as a structure; and to verify/deny my intuition regarding the ‘sheaves of bounded tanglings’ idea for lines.

I will say, the print version of this book is very nice. I have a softcover on a little 3d printed stand while I’m working and the print quality is very nice. The cover is colorful in a way that doesn’t scream “Overpriced undergrad Calculus Book” and is more of a “Someone might mistake this for a book about something that isn’t math.” Which I mean in the most complementary sense I can.

1034

I wouldn’t be surprised if this, too, ends up getting shelved for me to go do some algebra and topology, I have an Algebra by Hungerford which is not the GTM version that probably covers enough for my purposes and should be pretty light work. I have another book, Topology: A Categorical approach by Bradely et al, that I’ve worked through part of before and might be a decent way to extend HT’s Category theory and also rough in some Topology stuff.