On Fri, 13 May 2016, Hans Åberg wrote:

There may not be so many symbols: the “large operators" in the Tex Book, p. 435, though Unicode have more, and some others like √ U+221A for \sqrt.

If you want, you can collect such mappings in a separate module.

I could not make your code working - does it require a later LuaTex version (than 0.80.0)?

Here is a complete working example (OT: The location of the limit is still ugly with xits fonts)

\setupbodyfont[xits,10pt]

\appendtoks
     \catcode`∫=\activecatcode
     \letcharcode `∫ \int
\to \everymathematics
\setupmathematics[integral=nolimits]

Nolimits $\int_0^∞ f ω$, and $∫_0^∞ f ω$

\startformula
    \int_0^∞ f ω,\quad ∫_0^∞ f ω
\stopformula
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