Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.03766 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914238217322496 |
|---|---|
| author | Bianchi, Andrea Zhang, Adela Yiyu |
| author_facet | Bianchi, Andrea Zhang, Adela Yiyu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03766 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Universal property of graph cobordisms Bianchi, Andrea Zhang, Adela Yiyu Algebraic Topology 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. |
| title | Universal property of graph cobordisms |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2601.03766 |