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• CommentRowNumber1.
• CommentTimeNov 21st 2022

Started page.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeNov 21st 2022
• (edited Nov 21st 2022)

On formatting:

I have slightly adjusted the typesetting of the (co)limits by placing their indices below the arrow:

  $$A_{\square}[S] \;=\; \underset {\underset{ A'\subseteq A }{ \rightarrow }} {\lim} \; \underset {\underset{i}{\leftarrow}} {\lim} \; A'\big[S_{i}\big]$$


By the way, just by enclosing technical terms in double square brackets, they get automatically hyperlinked to their respective entries, which is much of what the point of the wiki is about.

This certainly works for basics like ring ([[ring]]), subring ([[subring]]), profinite integers ([[profinite integers]]) etc.

For something like “condensed $A$-modules” we can typeset as [[condensed module|condensed $A$-modules]] and then create an entry titled “condensed module”.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeNov 21st 2022
• (edited Nov 21st 2022)

By the way, do you mean to write “derived $\infty$-category”, or is this rather just “$\infty$-category”?

The question is whether you mean just the homotopy category. This matters later when the entry speaks about the map of hom-objects being an “isomorphism”. From looking (just) at Mann’s abstract, I suspect this is really meant to be an equivalence of hom-spaces (i.e. of hom-$\infty$-groupoids)?

• CommentRowNumber4.
• CommentTimeNov 21st 2022
Thanks for the fixes! I think it should be "derived $\infty$-category" (i.e. complexes of modules) and not just $\infty$-category. This is discussed in page 15 of Mann's arxiv preprint. Mann further gives 1.3 of Lurie's Higher Algebra as reference.
• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeNov 21st 2022

I see, thanks. So let’s say:

with pointer to “(infinity,1)-category of chain complexes”.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeNov 21st 2022

and so I have expanded the “the canonical map … is an isomorphism” to:

the canonical map of mapping objects … is an equivalence

• CommentRowNumber7.
• CommentTimeNov 22nd 2022

Added a brief sentence on globalization and added a section for coherent duality, to be filled in later.

• CommentRowNumber8.
• CommentTimeNov 22nd 2022

Added the statement of Theorem 11.1 (Coherent Duality) from Scholze’s Lectures on Condensed Mathematics. The statement is currently verbatim, and I am planning to make edits in the future to give it more context.

• CommentRowNumber9.
• CommentTimeNov 22nd 2022

Added section on the six operations.

• CommentRowNumber10.
• CommentTimeNov 24th 2022

Started a section on Mann’s application of solid modules.

• CommentRowNumber11.
• CommentTimeNov 24th 2022

• CommentRowNumber12.
• CommentTimeNov 25th 2022

Starting to add a little more detail for the six-functor formalism for solid modules. Will fill in more later.

• CommentRowNumber13.
• CommentTimeNov 25th 2022

Added mention of Mann’s p-torsion Riemann-Hilbert correspondence.

• CommentRowNumber14.