The 2-group of linear auto-equivalences of an abelian category and its Lie 2-algebra
Abstract
For any abelian category satsifying (AB5) over a separated, quasi-compact scheme S, we construct a stack of 2-groups () over the flat site of S. We will give a concrete description of () when is the category of quasi-coherent sheaves on a separated, quasi-compact scheme X over S. We will show that the tangent space () of () at the origin has a structure as a Lie 2-algebra.
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