PreprintCC BY 4.0arXiv
Cospan contexts and higher categories
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 Catn 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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BibTeX
@misc{riva2026cospan,
title = {{Cospan contexts and higher categories}},
author = {Lorenzo Riva},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24473},
eprint = {2610.24473},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24473},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cospan contexts and higher categories
AU - Lorenzo Riva
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24473
UR - https://arxiv.org/abs/2610.24473
AB - 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 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).
ER -