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arXiv · 2610.24473

Cospan contexts and higher categories

Lorenzo Riva
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Abstract

Motivated by the desire to turn the cobordism hypothesis (a statement about the universal property of some $n$-category of bordisms) into a $1$-categorical statement, we prove that all $n$-categories can be modeled by \emph{$n$-cospan contexts}: these are $1$-categories equipped with a collection of iterated cospans that satisfy a composition property in terms of pushouts. In particular, we construct an adjunction from $\mathsf{Cat}_n$ to the category of $n$-cospan contexts which simultaneously generalizes the $n$-fold span construction of Haugseng and the twisted arrow category construction (when $n = 1$).

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Lorenzo Riva. 2026-10-17. Cospan contexts and higher categories. https://arxiv.org/abs/2610.24473

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