Dear categoricist, Let I be the following small category : a a a --------> --------> --------> .. n n-1 n-2 ...... 0 --------> --------> --------> b b b with the relations a o a = a o b and b o a = b o b. Consider the category C of functors from I to the category of K-modules. How could we characterize the projective objects of C ? Any idea, any reference, is welcome. pg.