Limits as adjoint to constant functors Let us suppose that $C$ is a category where small limits are representable and $D$ is a small category. 
Let $F:Hom(D,C)\rightarrow C$ be the functor defined by $F(f)=\varprojlim f$. 
Is it true that $F$ has a right adjoint constant functor? Can someone please explain this to me? What about the unit and co-units here? 
Also, could someone please suggest me some nice introductory books on this stuff? I am finding it very confusing. 

No, $F$ has no right adjoint in general, but it has a left adjoint, which sends each object $c$ of $C$ to the constant functor in $\text{Hom}(D,C)$ that sends every object of $D$ to $c$.  
I'm probably old-fashioned, but I still think the best introductory book on category theory is Saunders Mac Lane's "Categories for the Working Mathematician".
