Higher Dimensional Homology Algebra II:Projectivity

Abstract

In this paper, we will prove that the 2-category (2-SGp) of symmetric 2-groups and 2-category ($\cR$-2-Mod) of $\cR$-2-modules(\cite{5}) have enough projective objects, respectively.

10 pages, 4 figures. This is the second paper of the series works on higher dimensional homology algebra. The first paper is "2-Modules and the Representation of 2-Rings\cite{4}". In the coming papers, we shall give the definition of injective object in the 2-category ($\cR$-2-Mod), prove that this 2-category has enough injective objects and develop the (co)homology theory of it