???if you take the cokernel of (x,y) : 1 -> 1+1 , then ???....

??something about ... dual of cokernel as extra stuff ...???...

but ...

??vague feeling... not describing this very well ...

??various versions of... question as to whether "good embedding" gives hoped-for syntactic algebroid ...??? ....

versions distinguished by "how much is nailed down" ... or something...

??something about ... ??some sort of tendency for nailing certain thing down to make it natural for nailing certain other thing down ... ???or something????...

?? something about complementary quotient object of sub-object ... ??? ....

??or something ???? ......