On Homological Dimensions in Some Functor Categories

In this paper, we investigate the homological properties of the functor categories $(\text{mod}{-}R, \text{Ab})$ and $((\text{mod}-R)^{\text{op}}, \text{Ab})$. Some new homological dimensions in these functor categories such as $FP$-projecive dimensions and cotorsion dimensions for functors and functor categories are introduced and studied. We also characterize functor categories of homological dimensions zero and explore the connections among some different homological dimensions.