Calligraphic symbols (\mathcal) are available in Unicode (https://en.wikipedia.org/wiki/Mathematical_operators_and_symbols_in_Unicode#Mathematical_Alphanumeric_Symbols_block) and are supported by other LaTeX input packages (https://github.com/clarkgrubb/latex-input). It will be really useful to include those here.
Could use \C<symbol> instead of \mathcal{<symbol>} as shorthand.