  In this paper we continue the project of generalizing tilting theory to the
category of contravariant functors $Mod(C)$, from a skeletally small
preadditive category $C$ to the category of abelian groups. We introduced the
notion of a a generalized tilting category $T$, and extended Happel's theorem
to $Mod(C)$. We proved that there is an equivalence of triangulated categories
$D^b (Mod(C))\cong Db (Mod(T))$. In the case of dualizing varieties, we proved
a version of Happel's theorem for the categories of finitely presented
functors. We also proved in this paper, that there exists a relation between
covariantly finite coresolving categories, and generalized tilting categories.
Extending theorems for artin algebras. In this article we consider the category
of maps, and relate tilting categories in the category of functors, with
relative tilting in the category of maps. Of special interest is the category
$mod(mod \Lambda)$ with $\Lambda$ an artin algebra.
