nLab David Penneys (changes)

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Selected writings

On monoidal enriched categories:

• Scott Morrison, David Penneys, Monoidal Categories Enriched in Braided Monoidal Categories, International Mathematics Research Notices 2019 11 June 2019 3527–3579 [[doi:10.1093/imrn/rnx217](https://doi.org/10.1093/imrn/rnx217), arXiv:1701.00567]

On topological phases of matter (with emphasis on monoidal category-machinery such as unitary fusion categories)

• David Penneys, Topological Phases of Matter (2021)

On G-crossed braided fusion categories via 3-categories:

• Corey Jones, David Penneys, David Reutter, A 3-categorical perspective on $G$-crossed braided categories, J. London Math. Soc. 107 1 (2023) 333-406 [[arXiv:2009.00405](https://arxiv.org/abs/2009.00405), doi:10.1112/jlms.12687]

On anyonic topological order in the Levin-Wen model:

• Jessica Christian, David Green, Peter Huston, David Penneys: A lattice model for condensation in Levin-Wen systems [[arXiv:2303.04711](https://arxiv.org/abs/2303.04711)]

On the Levin-Wen model as a gauge theory:

• Kyle Kawagoe, Corey Jones, Sean Sanford, David Green, David Penneys: Levin-Wen is a gauge theory: entanglement from topology [[arXiv:2401.13838](https://arxiv.org/abs/2401.13838)]

Introducing a notion of dagger $n$-categories:

• Giovanni Ferrer, Brett Hungar, Theo Johnson-Freyd, Cameron Krulewski, Lukas Müller, Nivedita, David Penneys, David Reutter, Claudia Scheimbauer, Luuk Stehouwer, Chetan Vuppulury, Dagger n-categories [[arXiv:2403.01651](https://arxiv.org/abs/2403.01651)]

On identifying $W^\ast$-categories with 2-Hilbert spaces:

• André Henriques, Nivedita, David Penneys: Complete $W^\ast$-categories [[arXiv2411.01678](https://arxiv.org/abs/2411.01678)]

On fusion 2-categories:

• Thibault Decoppet, Peter Huston, Theo Johnson-Freyd, Dmitri Nikshych, David Penneys, Julia Plavnik, David Reutter, Matthew Yu: The Classification of Fusion 2-Categories [[arXiv:2411.05907](https://arxiv.org/abs/2411.05907)]

On topological order described by braided fusion categories via local nets of observables in AQFT:

• Pieter Naaijkens, David Penneys, Daniel Wallick: Local topological order, Haag duality, and reflection positivity [arXiv:2605.10693]

On 2-Hilbert spaces:

• Giovanni Ferrer, Lukas Müller, David Penneys, Luuk Stehouwer: The many faces of higher Hilbert spaces [[arXiv:2606.11334](https://arxiv.org/abs/2606.11334)]