\startluacode
    mathematics.registerdomain {
        name       = "foo",
        parents    = { "bar" },
        characters = {
            [0x3A] = {
                char  = 0x2236,
                class = "inner"
            }
        }
    }
\stopluacode

\startTEXpage
    $a: b$\par
    \setupmathematics[domain=foo]$a: b$\par
    \mathematics[domain=foo]{a: b}\par
    \definemathematics[foo][domain=foo]\mathematics[foo]{a: b}\par
\stopTEXpage
