??so what about something about ... ???single-environment completeness theorem vs multi-environment .... or something ... ??did we have some sort of other jargon about this?? ???something about "duality" or something ?? .... ... ???.... ??anyway, some thing about some vague memory ... ??generalized gabriel-ulmer duality or something?? ... ??something about ... ??various kinds of limits and/or colimits ... ??sometimes centralizing each other, or something ?? ... ??something about geometric theories maybe fitting into this somehow?? ... ??though seems weird because geometric doctrine seems to need multi-environment model theory ... ??or something ... ???....