Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2211.08436

Gauging Noninvertible Defects: A 2-Categorical Perspective

Thibault D. Décoppet·Matthew Yu
View original source ↗Read source document ↗Export metadata ↓

Abstract

We generalize the notion of an anomaly for a symmetry to a noninvertible symmetry enacted by surface operators using the framework of condensation in 2-categories. Given a multifusion 2-category, potentially with some additional levels of monoidality, we prove theorems about the structure of the 2-category obtained by condensing a suitable algebra object. We give examples where the resulting category displays grouplike fusion rules and through a cohomology computation, find the obstruction to condensing further to the vacuum theory.

Explore related subjects

math.CThep-thmath-phmath.MPmath.QA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Thibault D. Décoppet, Matthew Yu. 2022-11-25. Gauging Noninvertible Defects: A 2-Categorical Perspective. https://doi.org/10.1007/s11005-023-01655-1

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Mixing Extriangulated Model Structures

Let $(\mathscr{C},\mathbb{E},\mathfrak{s})$ be a weakly idempotent complete extriangulated category. We generalize Cole's Theorem to construct a mixed admissible model structure $\mathcal{M}_m$ from two compatible admissible model structures relative to proper classes $ξ_1\subseteqξ_2$ of $\mathscr{C}$. We then explicitly characterize the cofibrant objects of $\mathcal{M}_m$. Finally, we apply these results to exact and triangulated categories, recovering and extending recent work on mixed model structures.

math.CT↗
arXiv2026

Characterizing (Co)Free Dagger Categories

For any category, there exists both a free dagger category and a cofree dagger category over it. A natural question to ask is: given a dagger category, how can we tell if it is free or cofree without specifying an external base category? In this paper, we provide characterizations of both free dagger categories and cofree dagger categories via internal dagger category structure. To characterize cofree dagger categories, we use rectangular bands and show that a dagger category is cofree if and only if it is enriched over rectangular bands. For free dagger categories, we define the notion of a zigzag dagger category, and then show that a dagger category is free if and only if it is a zigzag dagger category. We also show that free dagger categories can be characterized as the coalgebras of the induced comonad from the free dagger category adjunction, and similarly that cofree free dagger categories can be characterized as the algebras of the induced monad from the cofree dagger category adjunction.

math.CT↗
arXiv2026

A Counterexample to the Open Question on Object Ideals

We give a counterexample to completeness descent from ideal cotorsion pairs to their objects. A radical-square-zero algebra on the two-cycle gives a finite-dimensional example. The construction is intrinsically non-weakly-idempotent-complete.

math.CT↗