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Relative Invertibility and Full Dualizability of Finite Braided Tensor Categories
Thibault D. D\'ecoppet
https://arxiv.org/abs/2506.16241 https://

Relative Invertibility and Full Dualizability of Finite Braided Tensor Categories
Fix a finite symmetric tensor category $\mathcal{E}$ over an algebraically closed field. We derive an $\mathcal{E}$-enriched version of Shimizu's characterizations of non-degeneracy for finite braided tensor categories. In order to do so, we consider, associated to any $\mathcal{E}$-enriched finite braided tensor category $\mathcal{A}$ satisfying a mild technical assumption, a Hopf algebra $\mathbb{F}_{\mathcal{E}/\mathcal{A}}$ in $\mathcal{A}$. This is a generalization of Lyubashenko's univers…

The Braided Prairie: Six Nebraskan Literary Voices on Land, Life, and Legacy
The American Great Plains have produced a literary tradition as vast and complex as the landscape itself. Nebraska, with its braided rivers and endless horizons, stands at the heart of this tradition, having shaped some of the nation's most distinctive literary voices. From the rolling Sandhills to the fossil-rich badlands, from pioneer settlements to Native American territories, the state's…

The Braided Prairie: Six Nebraskan Literary Voices on Land, Life, and Legacy | David Boles, Blogs
The American Great Plains have produced a literary tradition as vast and complex as the landscape itself. Nebraska, with its braided rivers and endless horizons, stands at the heart of this traditi…

It's truth in advertising when the braided UHMWPE product page shows it unraveling! 🤣
I've learned that plasma lighters are great tools for cutting light gauge synthetic cord. They are basically small hot plasma knives that cut slowly. Works for UHMWPE, nylon, polyester, and more. Also PET cable sheath, which is otherwise highly motivated to spontaneously disassemble itself.

2-Group Symmetries of 3-dimensional Defect TQFTs and Their Gauging
Nils Carqueville, Benjamin Haake
https://arxiv.org/abs/2506.08178 https://

2-Group Symmetries of 3-dimensional Defect TQFTs and Their Gauging
A large class of symmetries of topological quantum field theories is naturally described by functors into higher categories of topological defects. Here we study 2-group symmetries of 3-dimensional TQFTs. We explain that these symmetries can be gauged to produce new TQFTs iff certain defects satisfy the axioms of orbifold data. In the special case of Reshetikhin-Turaev theories coming from $G$-crossed braided fusion categories $\mathcal C^\times_G$, we show that there are 0- and 1-form symmetri…

On the finite generation of the cohomology of bosonizations
Nicol\'as Andruskiewitsch, David Jaklitsch, Van C. Nguyen, Amrei Oswald, Julia Plavnik, Anne V. Shepler, Xingting Wang
https://arxiv.org/abs/2506.05267

On the finite generation of the cohomology of bosonizations
We use deformation sequences of (Hopf) algebras, extending the results of Negron and Pevtsova, to show that bosonizations of some suitable braided Hopf algebras by some suitable finite-dimensional Hopf algebras have finitely generated cohomology. In fact, our results are shown in more generality for smash products. As applications, we prove the bosonizations of some Nichols algebras (such as Nichols algebras of diagonal type, the restricted Jordan plane, Nichols algebras of direct sums of Jorda…

This https://arxiv.org/abs/2403.10366 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Graded Schur Lemma and a graded-monoidal structure for induced modules over graded-commutative algebras
We consider algebras and Frobenius algebras, internal to a monoidal category, that are graded over a finite abelian group. For the case that A is a twisted group algebra in a linear abelian monoidal category we obtain a graded generalization of the Schur Lemma for the category of induced A-modules. We further show that if the monoidal category is braided and A is commutative up to a bicharacter of the grading group, then the category of induced A-modules can be endowed with a graded-monoidal st…