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arxiv: 1905.06671 · v1 · pith:ZI6DBK5Dnew · submitted 2019-05-16 · 🧮 math.AT · math.CT

2-Segal objects and algebras in spans

classification 🧮 math.AT math.CT
keywords objectsalgebracategorysegalcalabi-yauinfinityspanspans
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We define a category parameterizing Calabi-Yau algebra objects in an infinity category of spans. Using this category, we prove that there are equivalences of infinity categories relating, firstly: 2-Segal simplicial objects in C to algebra objects in Span(C); and secondly: 2-Segal cyclic objects in C to Calabi-Yau algebra objects in Span(C).

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  1. Squares K-theory and 2-Segal spaces

    math.KT 2024-09 unverdicted novelty 7.0

    S_•-construction on stable proto-Waldhausen squares categories produces 2-Segal spaces.