Searcharxiv⌕ Search

arXiv subjects

Claudia I. Scheimbauer

Publications and source records attributed to Claudia I. Scheimbauer.

6 recordsLinked to original sources
arXiv2026

Fully local Reshetikhin-Turaev theories

Completing an arc of research initiated by Reshetikhin--Turaev and Witten, we construct fully local 3-dimensional topological field theories from non-degenerate braided fusion categories. We do so by defining a symmetric tensor enhancement $\mathrm{E}\mathbb{F}$ with full duals of the 3-category $\mathbb{F}$ of fusion categories, in which every Reshetikhin--Turaev theory has a point generator. This $\mathrm{E}\mathbb{F}$ is a direct sum of invertible $\mathbb{F}$-modules, indexed by a $μ_6$-extension of the Witt group of non-degenerate braided fusion categories. Similarly, we enhance the 3-category $S\mathbb{F}$ of fusion super-categories to a symmetric tensor 3-category $\mathrm{E} S\mathbb{F}$ with full duals, which is a sum of invertible $S\mathbb{F}$-modules, indexed by a $μ_{24}$-extension of the super-Witt group. The unit spectrum of $\mathrm{E}S\mathbb{F}$ is the connective cover of the Pontrjagin dual of $\mathbb{S}^{-3}$. We discuss tangential structures and central charges of the resulting TQFTs. We establish Spin-invariance of fusion super-categories, and relate SO-invariance structures to modular and spherical structures, confirming some conjectures from arXiv:1312.7188.

math.QA↗
arXiv2025

Assembly of Constructible Factorization Algebras

We provide a toolbox of extension, gluing, and assembly techniques for factorization algebras. Using these tools, we fill various gaps in the literature on factorization algebras on stratified manifolds, the main one being that constructible factorization algebras form a sheaf of symmetric monoidal $\infty$-categories. Additionally, we explain how to assemble constructible factorization algebras from the data on the individual strata together with module structures associated to the relative links; thus answering a question by Ayala. Along the way, we give detailed proofs of the following facts which are also of independent interest: constructibility is a local condition; the $\infty$-category of disks is a localization of any sufficiently fine poset of disks; constructibility implies the Weiss condition on disks; constructible factorization algebras are algebras for the $\infty$-operad of embedded disks. For each of these, variants or special cases already existed, but they were either incomplete or not general enough.

math.AT↗
arXiv2020

Comparison of Waldhausen constructions

In previous work, we develop a generalized Waldhausen $S_{\bullet}$-construction whose input is an augmented stable double Segal space and whose output is a unital 2-Segal space. Here, we prove that this construction recovers the previously known $S_{\bullet}$-constructions for exact categories and for stable and exact $(\infty,1)$-categories, as well as the relative $S_{\bullet}$-construction for exact functors.

math.AT↗
arXiv2018

2-Segal objects and the Waldhausen construction

In a previous paper, we showed that a discrete version of the $S_\bullet$-construction gives an equivalence of categories between unital 2-Segal sets and augmented stable double categories. Here, we generalize this result to the homotopical setting, by showing that there is a Quillen equivalence between a model category for unital 2-Segal objects and a model category for augmented stable double Segal objects which is given by an $S_\bullet$-construction. We show that this equivalence fits together with the result in the discrete case and briefly discuss how it encompasses other known $S_\bullet$-constructions.

math.AT↗
arXiv2017

2-Segal sets and the Waldhausen construction

It is known by results of Dyckerhoff-Kapranov and of Gálvez--Carrillo-Kock-Tonks that the output of the Waldhausen S.-construction has a unital 2-Segal structure. Here, we prove that a certain S.-functor defines an equivalence between the category of augmented stable double categories and the category of unital 2-Segal sets. The inverse equivalence is described explicitly by a path construction. We illustrate the equivalence for the known examples of partial monoids, cobordism categories with genus constraints and graph coalgebras.

math.AT↗