On abelian 2-categories and derived 2-functors

Abstract

This is an extended version of my earlier articel "Projective and injective objects in symmetric categorical groups. arXiv:1007.0121v1." Several new facts added, including the material on the derived 2-functors and the proof of the Gabriel-Mitchel theorem and the Morita theory for 2-rings.

We add a new section on the cohomology of 2-groups

References in corpus (3)

• Third Mac Lane cohomology via categorical rings
• Enrichments over symmetric Picard categories
• Projective and injective objects in symmetric categorical groups

Cited by in corpus (2)

• Cohomology with coefficients in stacks of Picard categories
• Higher Dimensional Homology Algebra III:Projective Resolutions and Derived 2-Functors in (2-SGp)