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Hamiltonian flow between standard module Lagrangians
Yujin Tong
https://arxiv.org/abs/2511.06431 https://arxiv.org/pdf/2511.06431 https://arxiv.org/html/2511.06431
arXiv:2511.06431v1 Announce Type: new
Abstract: In Aganagic's Fukaya category of the Coulomb branch of quiver gauge theory, the $T_\theta$-brane algebra gives a symplectic realization of the Khovanov-Lauda-Rouquier-Webster (KLRW) algebra, where each standard module is known to admit two Lagrangian realizations: the 'U'-shaped $T$-brane and the step $I$-brane. We show that the latter arises as the infinite-time limit of the Hamiltonian evolution of the former, thus serving as a generalized thimble. This provides a geometric realization of the categorical isomorphism previously established through holomorphic disc counting.
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Oriented Category Theory
David Gepner, Hadrian Heine
https://arxiv.org/abs/2510.10504 https://arxiv.org/pdf/2510.10504

Oriented Category Theory
We develop foundations for oriented category theory, an extension of $(\infty,\infty)$-category theory obtained by systematic usage of the Gray tensor product, in order to study lax phenomena in higher category theory. As categorical dimension increases, classical category-theoretic concepts generally prove too rigid or fully break down and must be replaced by oriented versions, which allow more flexible notions of naturality and coherence. Oriented category theory provides a framework to addre…

Instances of models of double-categorical theories
Kevin Carlson, Evan Patterson
https://arxiv.org/abs/2510.08861 https://arxiv.org/pdf/2510.08861

Instances of models of double-categorical theories
We contribute a chapter in common to categorical database theory and to the study of higher morphisms between double categories. The common thread here is the notion of instance, or right module, which we generalize from functors from a plain category into Set to the models of a (cartesian) double theory. This provides a concept of instance for such objects as a category equipped with a monad, or a (symmetric) multicategory, recovering the multifunctors into Set in the latter case. We also show…

An introduction to representations of p-adic groups
Jessica Fintzen
https://arxiv.org/abs/2510.08692 https://arxiv.org/pdf/2510.08692

An introduction to representations of p-adic groups
An explicit understanding of the (category of all smooth, complex) representations of p-adic groups provides an important tool not just within representation theory. It also has applications to number theory and other areas, and, in particular, it enables progress on various different forms of the Langlands program. In this write-up of the author's ECM 2024 colloquium-style talk, we will introduce p-adic groups and explain how the category of representations of p-adic groups decomposes into sub…

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Measure theory via Locales
Georg Lehner
https://arxi…

Replaced article(s) found for hep-th. https://arxiv.org/list/hep-th/new
[2/2]:
- An operator algebraic approach to fusion category symmetry on the lattice
David E. Evans, Corey Jones

Natural transformations between braiding functors in the Fukaya category
Yujin Tong
https://arxiv.org/abs/2511.10462 https://arxiv.org/pdf/2511.10462 https://arxiv.org/html/2511.10462
arXiv:2511.10462v1 Announce Type: new
Abstract: We study the space of $A_\infty$-natural transformations between braiding functors acting on the Fukaya category associated to the Coulomb branch $\mathcal{M}(\bullet,1)$ of the $\mathfrak{sl}_2$ quiver gauge theory. We compute all cohomologically distinct $A_\infty$-natural transformations $\mathrm{Nat}(\mathrm{id}, \mathrm{id})$ and $\mathrm{Nat}(\mathrm{id}, \beta_i^-)$, where $\beta_i^-$ denotes the negative braiding functor. Our computation is carried out in a diagrammatic framework compatible with the established embedding of the KLRW category into this Fukaya category. We then compute the Hochschild cohomology of the Fukaya category using an explicit projective resolution of the diagonal bimodule obtained via the Chouhy-Solotar reduction system, and use this to classify all cohomologically distinct natural transformations. These results determine the higher $A_\infty$-data encoded in the braiding functors and their natural transformations, and provide the first step toward a categorical formulation of braid cobordism actions on Fukaya categories.
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Compositional difference-in-differences for categorical outcomes
Onil Boussim
https://arxiv.org/abs/2510.11659 https://arxiv.org/pdf/2510.11659

Compositional difference-in-differences for categorical outcomes
In difference-in-differences (DiD) settings with categorical outcomes, treatment effects often operate on both total quantities (e.g., voter turnout) and category shares (e.g., vote distribution across parties). In this context, linear DiD models can be problematic: they suffer from scale dependence, may produce negative counterfactual quantities, and are inconsistent with discrete choice theory. We propose compositional DiD (CoDiD), a new method that identifies counterfactual categorical quant…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Measuring Comodules and Enrichment
Martin Hyland, Ignacio Lopez Franco, Christina Vasilakopoulou

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- On the straightening of every functor
Thomas Blom
https://

Stranding $\mathfrak{sl}_n$ webs
Heather M. Russell, Julianna Tymoczko
https://arxiv.org/abs/2510.12035 https://arxiv.org/pdf/2510.12035

Stranding $\mathfrak{sl}_n$ webs
Webs are a kind of planar, directed, edge-labeled graph that encode invariant vectors for quantum representations of $\mathfrak{sl}_n$. The theory of webs developed organically for $\mathfrak{sl}_2$, where they are also known as noncrossing matchings and the Temperley-Lieb algebra, before being formalized by Kuperberg for $\mathfrak{sl}_2$ and $\mathfrak{sl}_3$ as the morphisms in a diagrammatic categorification of quantum representations called the spider category. Various models extend webs t…

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Homological epimorphisms in functor categories and singularity categories
Juan Andr\'es Orozco Guti\'errez, Valente Santiago Vargas

The fundamental junk theorem of material set theory: every discrete category is concrete.

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Arrow algebras
Benno van den Berg, Marcus Briet
https://

[2025-10-15 Wed (UTC), 2 new articles found for math.CT Category Theory]
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[2025-10-14 Tue (UTC), 5 new articles found for math.CT Category Theory]
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[2025-10-13 Mon (UTC), 1 new article found for math.CT Category Theory]
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