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.
Cyclic polytopes, orientals, and correspondences: some aspects of higher Segal spaces
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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.
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2025 1verdicts
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Higher Segal spaces and partial groups
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.