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Given a concrete category C, with objects denoted Obj(C), and an equivalence relation ~ on Obj(C) given by morphisms in C. The moduli set for Obj(C) is the set of equivalence classes with respect to ~; denoted Iso(C). When Iso(C) is an object in the category Top, then the moduli set is called a moduli space.
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fundamental group of moduli spaces of sheaves
I am considering moduli spaces of sheaves on irreducible holomorphic symplectic manifolds.
I haven't seen a general theory to describe the fundamental group of moduli spaces of sheaves yet. Is there s …