Cyclic polytopes, orientals, and correspondences: some aspects of higher Segal spaces

2025/05/04 by Dyckerhoff, Tobias · 1 citation
#Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.02051

Abstract

We discuss the role of higher Segal spaces at the interface of cyclic polytopes, orientals, and higher correspondences. Along the way we review examples from algebraic K-theory, show how cyclic polytopes provide a geometric model for the definition of orientals, and establish a characterization of higher Segal spaces as lax monadic structures in higher correspondence categories.

Cited by

• Coskeletality and the higher Segal conditions

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• Cyclic Segal Spaces
• Higher Segal structures in algebraic K-theory
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