bigroupoid valued functors

Hi all, In the following let Bigpd denote the _category_ of bigroupoids and 2-functors. I have a category C with a full subcategory i:D --> C and a pair of functors P_C: C --> Bigpd P_D: D --> Bigpd and a natural transformation t : P_D => P_C\circ i. The components of t are biequivalences, and in fact (non-strict) inclusions of sub-bigroupoids. I would like to know if it is possible to define a functor P' : C --> Bigpd that agrees (on objects) with P_D on D and with P_C on the rest of C. Cheers, David [For admin and other information see: http://www.mta.ca/~cat-dist/ ]