After a little snafu with python packages over the last few days, the Stacks project is now updated with your latest comments incorporated. Many thanks to Alex Scheffeling, Zhiyu Zhang, and David Holmes for their help in responding to comments.

Please keep leaving comments. Please be as precise as you can. From top to bottom the most valuable comments are

- Pointing out mathematical errors in proofs.
- Pointing out specific steps in a proof you do not understand.
- Pointing out typos which make it harder to understand the mathematics, e.g., if symbols are mixed up or if the arrows point in the wrong direction.
- Pointing out that a reference is to the wrong tag.
- Precise suggestions as to how to clarify a proof.
- Alternative proofs, written out in detail and checked to not use forward references.
- Spelling errors.
- Punctuation.
- Whitespace errors:)

The reason that alternative proofs are so low on this list is that of course almost every mathematical result can be proven in a 100 different ways.

Thanks very much for helping out!