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Two-dimensional categorified Hall algebras

By Mauro Porta and Francesco Sala
In the present paper, we introduce two-dimensional categorified Hall algebras of smooth curves and smooth surfaces. A categorified Hall algebra is an associative monoidal structure on the stable \(\infty\)-category \(\mathsf{Coh}^{\mathsf{b}}(\mathbb{R}\mathcal{M})\) of complexes of sheaves with bounded coherent cohomology on a derived moduli stack \(\mathbb{R}\mathcal{M}\). In the surface case, \(\mathbb{R}\mathcal{M}\) is... Show more
April 3, 2020
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Two-dimensional categorified Hall algebras
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