Functor Categories as Topoi

Consider the category of functors between two categories $E:=D^C$, with D being Sets.  It may be shown that E is complete and co-complete due to the fact Sets is; thinking of each object in E as a map from C to Sets, in the sense of evaluation, it can be shown that $(\varinjlim F_i) (C)= \varinjlim F_i(C)$ where $F_i$ are objects in E.  In particular $-\times E: E \rightarrow E$ commultes with both types of limits.  

Essentially E inheriting Sets' properties, similarly it can be shown that it is abelian, with enough injective objects (again see See Tamme).   

On objects A of E, PE(A) defined to be the set of subfunctors $Hom_E(-,A)xE$ is a functor with values in E, and the subfunctors FxE are in bijection with the morphisms in Nat(F,PE).  Hence E is a topos.  

The Functor category E as described above is called a presheaf, and in the case of a locally small category, via a Yoneda Embedding it may be though of as enlarging an arbitrary category C in such a way, that the enriched C will be complete, co-complete, abelian and posses enough injectives.