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

Tobias Dyckerhoff

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

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arxiv 2505.02051 v2 pith:HSNZ6NXD submitted 2025-05-04 math.AT math.CT

Tobias Dyckerhoff This is my paper · ORCID

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keywords highercyclicorientalspolytopessegalspacescorrespondencesalgebraic

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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.

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Higher Segal spaces and partial groups
math.GR 2025-07 conditional novelty 7.0 of 10

The higher Segal degree of a partial groupoid equals the Helly number of the closure space of a characteristic action, and the method gives explicit degrees for punctured Weyl groups.

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