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

TL;DR

This paper develops the theory of injective resolutions and derived 2-functors within the context of higher-dimensional homology algebra for $ ext{R}$-2-modules, extending classical homological concepts to 2-categories.

Contribution

It introduces the construction of injective resolutions and the definition of right derived 2-functors for $ ext{R}$-2-modules, advancing higher homological algebra.

Findings

Constructed injective resolutions for $ ext{R}$-2-modules

Defined the right derived 2-functor in this context

Explored properties of the derived 2-functor

Abstract

In this paper, we will construct the injective resolution of any $\cR$-2-module, define the right derived 2-functor, and give some related properties of the derived 2-functor in ($\cR$-2-Mod).