One had better take care to note explicitly how to compose maps to and from the newly adjoined "zero object", if following Yetter's idea,
The previous suggestion of considering functors to D + 1 was a false start for reasons Fred and Uwe pointed out, but it suggests a better approach: consider functors to the category D~ formed from D by freely adjoining a zero object. Arrows not in S now have somewhere to go (the zero arrow with the appropriate source and target).
For, given a and b objects in D and writing z for the newly adjoined zero object, what are we to take for compositions a --> * --> b ? Or were we also to adjoin "zero maps" z_(a,b) to each existing homset D(a, b), and then set these compositions all equal to those new zero maps? That suggests Yetter really meant to propose forming the free *pointed* category with zero object freely engendered by D ... or maybe that's what his words already meant to convey? Apologies if I was deaf to that tone :-) . Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]