David Alexander Jaklitsch

• Jaklitsch, David Alexander & Yamashita, Makoto (2026). The braided monoidal structure of tube algebra representations. Theory and Applications of Categories. 45(49), p. 2115–2152. doi: https:/tac.mta.ca/tac/volumes/45/49/45-49abs.html. Full text in Research Archive Show summary

  We consider the tube algebra of a spherical semisimple multitensor category X, and construct a braided monoidal structure with twist for its representations. We further show that this category is braided tensor equivalent with the Drinfeld center of the ind-category of X, extending the well-known linear equivalence.

• Jaklitsch, David Alexander & Yadav, Harshit (2026). ⊗-Frobenius Functors and Exact Module Categories. International Mathematics Research Notices (IMRN). ISSN 1073-7928. 2026(8). doi: 10.1093/imrn/rnag065. Full text in Research Archive
• Andruskiewitsch, Nicolás; Jaklitsch, David Alexander; Nguyen, Van C.; Oswald, Amrei; Plavnik, Julia & Shepler, Anne V. [Show all 7 contributors for this article] (2026). On the finite generation of the cohomology of bosonizations. Journal of Algebra. ISSN 0021-8693. 691, p. 741–780. doi: 10.1016/j.jalgebra.2025.10.057. Full text in Research Archive Show summary

  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 Jordan blocks plus points labeled with 1), by some suitable finite-dimensional Hopf algebras, have finitely generated cohomology, recovering some known results as well as providing new examples.

• Fuchs, Jürgen; Galindo, César; Jaklitsch, David Alexander & Schweigert, Christoph (2025). Spherical Morita contexts and relative Serre functors. Kyoto Journal of Mathematics. ISSN 2156-2261. 65(3), p. 537–594. doi: 10.1215/21562261-2024-0021. Full text in Research Archive Show summary

  The Morita context provided by an exact module category over a finite tensor category gives a two-object bicategory with duals. Right and left duals of objects in the module category are given by internal Homs and coHoms, respectively. We express the double duals in terms of relative Serre functors, which leads to a Radford isomorphism for module categories. There is a bicategorical version of the Radford S4 theorem: on the bicategory of a Morita context, the relative Serre functors assemble into a pseudo-functor, and the Radford isomorphisms furnish a trivialization of the square of this pseudo-functor (i.e., of the fourth power of the duals). We also show that the Morita bicategories coming from pivotal exact module categories are pivotal as bicategories, leading to the notion of pivotal Morita equivalence. This equivalence of tensor categories amounts to the equivalence of their bicategories of pivotal module categories. Furthermore, we introduce the notion of a spherical module category; it ensures that all categories in the Morita context of a spherical module category are spherical. Our results are motivated by and have applications to topological field theory.

• Fuchs, Jürgen; Galindo, César; Jaklitsch, David Alexander & Schweigert, Christoph (2025). A manifestly Morita-invariant construction of Turaev-Viro invariants. Quantum Topology. ISSN 1663-487X. doi: 10.4171/qt/234. Full text in Research Archive

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• Jaklitsch, David Alexander (2026). Levin-Wen model and tensor product of Tube algebra representations. Full text in Research Archive
• Jaklitsch, David Alexander (2026). The braided monoidal structure of Tube algebra representations. Full text in Research Archive
• Jaklitsch, David Alexander (2026). ⊗-Frobenius functors and exact module categories. Full text in Research Archive
• Jaklitsch, David Alexander (2025). Frobenius functors and exact module categories. Full text in Research Archive
• Jaklitsch, David Alexander (2025). A manifestly Morita-invariant construction of Turaev–Viro invariants. Full text in Research Archive
• Jaklitsch, David Alexander (2025). ⊗-Frobenius functors and exact module categories. Full text in Research Archive
• Jaklitsch, David Alexander (2025). A bicategorical state sum construction of Turaev-Viro invariants. Full text in Research Archive
• Jaklitsch, David Alexander (2025). Frobenius functors and pivotal comodule algebras. Full text in Research Archive Show summary

  A tensor functor between tensor categories can have isomorphic adjoint functors. We define a notion of Frobenius functors that accounts for the extra structure of bimodule categories. This condition will allow for the transport of unimodular and pivotal structures of module categories, thereby producing examples of Frobenius algebras. The purpose of the talk is to present this procedure in the context of Hopf algebras and pivotal co-module algebras.

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