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

TL;DR

This paper develops the theory of projective resolutions and derived 2-functors within the context of higher-dimensional homology algebra, specifically for $ $-2-modules, expanding the algebraic framework into higher categories.

Contribution

It introduces the construction of projective resolutions and the definition of derived 2-functors for $ $-2-modules, advancing higher homological algebra.

Findings

Constructed projective resolutions for $ $-2-modules

Defined derived 2-functors and explored their properties

Extended homological algebra into higher categorical settings

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.