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Thanks for adding good stuff!
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 -modules” we can typeset as [[condensed module|condensed $A$-modules]] and then create an entry titled “condensed module”.
By the way, do you mean to write “derived -category”, or is this rather just “-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--groupoids)?
I see, thanks. So let’s say:
… the (“derived”) -category of chain complexes of…
with pointer to “(infinity,1)-category of chain complexes”.
and so I have expanded the “the canonical map … is an isomorphism” to:
the canonical map of mapping objects … is an equivalence
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