??something about "structure / semantics adjointness" in somewhat general doctrine setting ... ???

d doctrine ....

e "family" of d-environments ... ?? (2,1)-fr into semantic (2,1) cat of d ...

s pre-stack on e ... ???or something ????....

.... ???....


???something about ... "universal example of theory of which given "potential model" is actual model" ... ??or something ...

??decategorification "universal example of system of equations of which given "potential solution" is actual solution" ... ???something about "cyclic subalgebra generated by x" or something, and so forth ... ???

??something about "clone" of x ... ???...

???something about ... ?? given doctrine d extending the doctrine of categories, and given functor into underlying category of d-environment ... ???...

??what about something about "diagram theory" here ?? ... or something ... ???...