All Outputs (6)

Planar diagrammatics of self-adjoint functors and recognizable tree series (2023)
Journal Article
Khovanov, M., & Laugwitz, R. (2023). Planar diagrammatics of self-adjoint functors and recognizable tree series. Pure and Applied Mathematics Quarterly, 19(5), 2409-2499. https://doi.org/10.4310/pamq.2023.v19.n5.a4

A pair of biadjoint functors between two categories produces a collection of elements in the centers of these categories, one for each isotopy class of nested circles in the plane. If the centers are equipped with a trace map into the ground field, t... Read More about Planar diagrammatics of self-adjoint functors and recognizable tree series.

Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras (2023)
Journal Article
Hannah, S., Laugwitz, R., & Ros Camacho, A. (2023). Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras. Symmetry, Integrability and Geometry: Methods and Applications, 19, Article 075. https://doi.org/10.3842/sigma.2023.075

We construct a separable Frobenius monoidal functor from Z Vect ω| H H to Z Vect ω G for any subgroup H of G which preserves braiding and ribbon structure. As an application, we classify rigid Frobenius algebras in Z Vect ω G , recovering the classif... Read More about Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras.

Constructing Non-semisimple Modular Categories with Local Modules (2023)
Journal Article
Laugwitz, R., & Walton, C. (2023). Constructing Non-semisimple Modular Categories with Local Modules. Communications in Mathematical Physics, 403, 1363-1409. https://doi.org/10.1007/s00220-023-04824-4

We define the class of rigid Frobenius algebras in a (non-semisimple) modular category and prove that their categories of local modules are, again, modular. This generalizes previous work of Kirillov and Ostrik (Adv Math 171(2):183–227, 2002) in the... Read More about Constructing Non-semisimple Modular Categories with Local Modules.

Indecomposable objects in Khovanov–Sazdanovic's generalizations of Deligne's interpolation categories (2023)
Journal Article
Flake, J., Laugwitz, R., & Posur, S. (2023). Indecomposable objects in Khovanov–Sazdanovic's generalizations of Deligne's interpolation categories. Advances in Mathematics, 415, Article 108892. https://doi.org/10.1016/j.aim.2023.108892

Khovanov and Sazdanovic recently introduced symmetric monoidal categories parameterized by rational functions and given by quotients of categories of two-dimensional cobordisms. These categories generalize Deligne's interpolation categories of repres... Read More about Indecomposable objects in Khovanov–Sazdanovic's generalizations of Deligne's interpolation categories.

A categorification of cyclotomic rings (2023)
Journal Article
Laugwitz, R., & Qi, Y. (2023). A categorification of cyclotomic rings. Quantum Topology, 13(3), 539-577. https://doi.org/10.4171/qt/172

For any natural number n≥2, we construct a triangulated monoidal category whose Grothendieck ring is isomorphic to the ring of cyclotomic integers On​. This construction provides an affirmative resolution to a problem raised by Khovanov in 2005.

The indecomposable objects in the center of Deligne's category Rep St (2023)
Journal Article
Flake, J., Harman, N., & Laugwitz, R. (2023). The indecomposable objects in the center of Deligne's category Rep St. Proceedings of the London Mathematical Society, 126(4), 1134-1181. https://doi.org/10.1112/plms.12509

We classify the indecomposable objects in the monoidal center of Deligne's interpolation category Rep St by viewing Rep St as a model‐theoretic limit in rank and characteristic. We further prove that the center of Rep St is semisimple if and only if... Read More about The indecomposable objects in the center of Deligne's category Rep St.