Higher Dimensional Homology Algebra IV:Projective Resolutions and Derived 2-Functors in ($\cR$-2-Mod)

Abstract

In this paper, we will construct the projective resolution of any $\cR$-2-module, define the derived 2-functor and give some related properties of the derived 2-functor.

17pages, 32 figures, This is the fourth paper of the series of our works on higher dimensional homological algebra. In the coming papers, we shall define the right derived 2-functor in the 2-categories (2-SGp) and ($\cR$-2-Mod), and give some relations of left derived 2-functors and right derived 2-functors