As a simple statement, I suppose “Dorian is a minor mode“ is no problem, but this is two different statements.
If one did happen to encounter “Modes are categorized (“loosely” changes nothing) by their root triad”, one has encountered incompetence. One thing one learns with really knowing is to recognize correct vs incorrect. The known issue of this mistake, in believing you knew when in fact you didn’t, is the thing that got David Dunning famous. You have to have the actual competence to know your actual competence.
(*: <Ionian> does not necessarily even suggest Leading Tone to 1; <Major key> does tend to suggest if not rather demand it. A mode is not a key.)