Abstract
In this section, we explain how to extract associative algebras from 2-Segal objects by means of theories with transfer. This procedure, applied to Waldhausen spaces, recovers various variants of Hall algebras, such as classical Hall algebras, derived Hall algebras, and motivic Hall algebras. Applying a theory with transfer to other 2-Segal spaces, we obtain classically known algebras, such as Hecke algebras, but also new algebras, such as the ones associated to the cyclic nerve of a category.
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