arXiv subjects

Tim Lüders

Publications and source records attributed to Tim Lüders.

3 recordsLinked to original sources

arXiv2026

Relative and lax volutive categories

In this paper we introduce the notion of a relative volutive (higher) category, specializing to the notion of a lax volutive (higher) category. Our primary motivation to study these objects is the following: while any rigid symmetric monoidal category admits a volutive structure, any closed symmetric monoidal category admits a lax volutive structure. We develop some of the basic theory of relative volutive categories and provide several equivalent formulations of lax volutive categories. We then study examples of interest, including categories of complete bornological vector spaces and modules over star-rings. We will also separately discuss unbounded operators between Hilbert spaces and Morita 2-categories, the latter of which in the context of fully closed symmetric monoidal 2-categories.

math.CT↗

arXiv2025

Orbifolds, higher dagger structures, and idempotents

The orbifold/condensation completion procedure of defect topological quantum field theories can be seen as carrying out a lattice or state sum model construction internal to an ambient theory. In this paper, we propose a conceptual algebraic description of orbifolds/condensations for arbitrary tangential structures in terms of higher dagger structures and higher idempotents. In particular, we obtain (oriented) orbifold completion from (framed) condensation completion by using a general strictification procedure for higher dagger structures which we describe explicitly in low dimensions; we also discuss the spin and unoriented case. We provide several examples of higher dagger categories, such as those associated to state sum models, (orbifolds of) Landau--Ginzburg models, and truncated affine Rozansky--Witten models. We also explain how their higher dagger structures are naturally induced from rigid symmetric monoidal structures, recontextualizing and extending results from the literature.

math.QA↗

arXiv2025

Real Twistings are 2-Line Bundles

We construct and study a bicategory of super 2-line bundles over graded Lie groupoids, providing a unified framework for geometric models of twistings of (real) K-theory. The core of our work is to exhibit a wide range of models from the literature as special cases, among them several variants of bundle gerbes (real/equivariant/Jandl), Freed-Moore's twisted groupoid extensions, Freed-Hopkins-Teleman's K-theory twistings, Moutuou's real twistings, Freed's invertible algebra bundles, and Distler-Freed-Moore's orientifold twistings.

math.AT↗