article · ArXiv.org · 2026

Universal property of graph cobordisms

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Abstract

We exhibit the symmetric monoidal $\infty$-category $\mathrm{GrCob}$ of graph cobordisms between spaces as a full $\infty$-subcategory of the $\infty$-category $\mathrm{Psh}(\mathrm{Gr})$ of presheaves over $\mathrm{Gr}$, where $\mathrm{Gr}$ is the symmetric monoidal $\infty$-category of graph cobordisms between finite sets. We also describe a universal property for $\mathrm{GrCob}$: it is, in a suitable sense, the free symmetric monoidal extension of $\mathrm{Gr}$ endowed with the factorization homology $\int_X*$ of the universal $\mathbf{E}_\infty$-Frobenius algebra for all spaces $X$. As a corollary, we identify the space of universal natural operations on the factorization homologies, in particular the Hochschild homology, of $\mathbf{E}_\infty$-Frobenius algebras.

Cite this paper

APA 7

Bianchi, A., & Zhang, A. Y. (2026). Universal property of graph cobordisms. ArXiv.org.

MLA 9

Bianchi, Andrea, and Adela Yiyu Zhang. “Universal property of graph cobordisms.” ArXiv.org, 2026.

Chicago

Bianchi, Andrea, and Adela Yiyu Zhang. 2026. “Universal property of graph cobordisms.” ArXiv.org.

Harvard

Bianchi, A. and Zhang, A.Y. (2026) ‘Universal property of graph cobordisms’, ArXiv.org.

BibTeX

@article{bianchi2026universal,
  title = {{Universal property of graph cobordisms}},
  author = {Bianchi, Andrea and Zhang, Adela Yiyu},
  journal = {ArXiv.org},
  year = {2026}
}

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