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Cyclic polytopes, orientals, and correspondences: some aspects of higher Segal spaces (2505.02051v2)
Published 4 May 2025 in math.AT and math.CT
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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