Higher Dimensional Homology Algebra III:Projective Resolutions and Derived 2-Functors in (2-SGp)

Abstract

In this paper, we will define the derived 2-functor by projective resolution of any symmetric 2-group, and give some related properties of the derived 2-functor.

30 pages, 50 figures. This is the third paper of the series of our works on higher dimensional homological algebra. In the coming papers, we define the right derived 2-functor in the 2-categories (2-SGp) and ($\cR$-2-Mod). In this version, we correct some errors in last version, add more results, such as 2-chain homotopy, its related results, etc