Hi,
Join, left semi join, and right semi join are available with \Join, \ltimes, and \rtimes respectively. In KaTeX, you cannot install packages. This makes the outer joins a bit more difficult. You can use either the unicode characters for them (?, ?, ?) or try to typeset them with something like this:
\def\ojoin{\rule[0.0ex]{0.25em}{0.1ex}\mathllap{\rule[1.1ex]{0.25em}{0.1ex}}}
\def\leftouterjoin{\mathrel{\ojoin\kern{-5.8mu}\Join}}
\def\rightouterjoin{\mathrel{\Join\kern{-5.8mu}\ojoin}}
\def\fullouterjoin{\mathrel{\ojoin\kern{-5.8mu}\Join\kern{-5.8mu}\ojoin}}
a \Join b \\
a \ltimes b \\
a \rtimes b \\
a \leftouterjoin b \\
a \rightouterjoin b \\
a \fullouterjoin b
Currently there’s no way in this plugin to create global definitions. It’s something that might be nice to have in a future version.