Comma categories

Dear category theorists, I have two questions concerning comma categories. If C is a category with a terminal object *, is the comma category (C,*) consisting of arrows from C to * isomorphic to the category C itself? If this is true, the same should apply to the dual case with an initial object. The category sSet of simplicial sets is the category of functors from the opposite delta category Delta^op to Set. The category of pointed simplicial sets sSet* is defined as the comma category (delta0, sSet), where delta0=hom(-,[0]). Is sSet* isomorphic to the category of functors from ([0],Delta)^op to Set? Thank you in advance for any help. Tony [For admin and other information see: http://www.mta.ca/~cat-dist/ ]