Culf maps and edgewise subdivision
Publikation: Working paper › Preprint › Forskning
Dokumenter
- 2210.11191v1
769 KB, PDF-dokument
We show that, for any simplicial space $X$, the $\infty$-category of culf maps over $X$ is equivalent to the $\infty$-category of right fibrations over $\operatorname{sd}(X)$, the edgewise subdivision of $X$ (when $X$ is a Rezk complete Segal space or 2-Segal space, this is the twisted arrow category of $X$). We give two proofs of independent interest; one exploiting comprehensive factorization and the natural transformation from the edgewise subdivision to the nerve of the category of elements, and another exploiting a new factorization system of ambifinal and culf maps, together with the right adjoint to edgewise subdivision. Using this main theorem, we show that the $\infty$-category of decomposition spaces and culf maps is locally an $\infty$-topos.
Originalsprog | Udefineret/Ukendt |
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Status | Udgivet - 20 okt. 2022 |
Eksternt udgivet | Ja |
Bibliografisk note
Appendix coauthored with Jan Steinebrunner. 53 pages
- math.AT, math.CT, 18N50, 55U10, 18N45, 18N60, 18N55, 18A32
Forskningsområder
ID: 373038342