The 2-group of linear auto-equivalences of an abelian category and its Lie 2-algebra

2009/10/29 by Xinwen Zhu, Zhu, Xinwen · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0910.5699

openalex publication_date 2009/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any abelian category \calC satsifying (AB5) over a separated, quasi-compact scheme S, we construct a stack of 2-groups \GL(\calC) over the flat site of S. We will give a concrete description of \GL(\calC) when \calC is the category of quasi-coherent sheaves on a separated, quasi-compact scheme X over S. We will show that the tangent space \gl(\calC) of \GL(\calC) at the origin has a structure as a Lie 2-algebra.

Citations

• Gerbal Representations of Double Loop Groups

Cited by

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

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