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Register a new userIterated spans and classical topological field theories
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Authors
Rune Haugseng
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We construct higher categories of iterated spans, possibly equipped with extra structure in the form of local systems, and classify their fully dualizable objects. By the Cobordism Hypothesis, these give rise to framed topological quantum field theories, which are the fram
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We show that Segal spaces, and more generally category objects in an $infty$-category $mathcal{C}$, can be identified with associative algebras in the double $infty$-category of spans in $mathcal{C}$. We use this observation to prove that having identities is a property of a non-unital $(infty,n)$-category.
While not obvious from its initial motivation in linear algebra, there are many context where iterated traces can be defined. In this paper we prove a very general theorem about iterated 2-categorical traces. We show that many Lefschetz-type theorems in the literature are consequences of this result and the new perspective we provide allows for immediate spectral generalizations.
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