?? reflective (???full ???? ...) subcategories of _graph_ ??? .....

??? "codiscrete graphs" .... codiscretization left adjoint to inclusion functor ... ????....

??? closed under limits ???....

?? fullness does seem intuitively to help a lot in narrowing down the list of closed-under-limits subcategories ... ???....

??? some sort of "birkhoff theorem" ideas here ??? ....

?? some idea about "secondary law" ... ???vs "secondary operation" ?? .... ?? "implication" ...??? ... "horn clause" ??? .... ???? .... ??? .... ??? is composite of monadic functors between posets again monadic ??? .... ??? ....???? ....


??again, grothendieck quasitopology as possibly interesting special case here ... including case where quasisheaves form a complete heyting algebra (??...) ... ???....

???full complete (??...) continuously included subcategory generated by single graph ... ??? might want to consider even simpler examples... ??n-stage trees ??? .....