Relative homological coalgebras

We study classes of relative injective and projective comodules and extend well-known results about projective comodules given in [7]. The existence of covers and envelopes by these classes of comodules is also studied and used to characterize the projective dimension of a coalgebra. We also compare this homological coalgebra with the very intensively studied homological algebra of the dual algebra (see [5]). This revised version was published online in June 2006 with corrections to the Cover Date.