so let r1 be a commutative ring, r2 a commutative r1-algebra,and x an r2-algebroid, equipped with for each "tame" r1-algebroid morphism m : [a,_r1-mod_] -> [b,_r1-mod_] a corresponding r2-algebroid morphism m' : [a,x] -> [b,x], and for each natural transformation between m1 and m2 a corresponding one between m1' and m2' ... and so forth.

for example if r1 = r2 = z and "tame" is defined the right way, then i think that x is an abelian category...

now consider [c,x] where c is some algebroid. in general this needn't have the same structure... ???....