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

TL;DR

This paper introduces the concept of derived 2-functors via projective resolutions in symmetric 2-groups, expanding the framework of higher homology algebra.

Contribution

It defines derived 2-functors using projective resolutions in symmetric 2-groups and explores their fundamental properties.

Findings

Established the definition of derived 2-functors in symmetric 2-groups.

Proved key properties of these derived 2-functors.

Extended homological algebra concepts to higher categorical structures.

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.