2-Segal sets are shown to correspond one-to-one, up to isomorphism, with pseudomonoids in the bicategory of spans, using a graphical proof that avoids higher category theory.
Combinatorial examples and applications of 2-Segal sets
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We give an introduction to the theory of 2-Segal sets, and two of the main applications of them: Hall algebras and a discrete version of Waldhausen's $S_\bullet$-construction. We present several combinatorial examples and how these constructions can be applied to them.
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2-Segal sets and pseudomonoids in the bicategory of spans
2-Segal sets are shown to correspond one-to-one, up to isomorphism, with pseudomonoids in the bicategory of spans, using a graphical proof that avoids higher category theory.