Projective and injective objects in symmetric categorical groups

2010/07/01 by Teimuraz Pirashvili, Pirashvili, Teimuraz · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1007.0121

openalex publication_date 2010/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the 2-category of symmetric categorical groups have enough projective and injective objects. This was conjectured by Bourn and Vitale in 2002 and was anounced recently by Fang Huang, Shao-Han Chen, Wei Chen and Zhu-Jun Zheng in arXiv:1006.4677 with wrong proof.

Citations

• Higher Dimensional Homology Algebra II:Projectivity
• Third Mac Lane cohomology via categorical rings

Cited by

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

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