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I have changed
that generalize posets …
to
that generalize (categorify) the notion of posets…
Notice that you don’t need to code as
$n$-[[n-poset|posets]]
The parser is fine with
[[n-poset|$n$-posets]]
In particular the code
$2$-[[2-category|categories]]
would probably better be
[[2-category|$2$-categories]]
or, more simply, just
[[2-categories]]
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