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Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
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- The Category of Hypergroups: seeking for a generalized version of Abelian Categories
Kaique Matias de Andrade Roberto, Ana Luiza Ten\'orio

Semi-orthogonality in Fukaya-Seidel mirrors to blowups of abelian varieties
Catherine Cannizzo, Sara Venkatesh
https://arxiv.org/abs/2508.06379 https://arx…

Semi-orthogonality in Fukaya-Seidel mirrors to blowups of abelian varieties
We prove a categorical homological mirror symmetry result for a blow-up of an abelian surface times $\mathbb{C}$, on the complex side. Specifically, the first author's paper arXiv:1908.04227 provides evidence for homological mirror symmetry for genus 2 curves $Σ_2$ on the complex side, where $Σ_2$ is a hypersurface in an abelian surface $V \cong T^4$. To obtain a mirror to $Σ_2$, the generalized SYZ approach arXiv:hep-th/0002222, arXiv:1205.0053 was used. That is, $(\text{Bl}_{Σ_2 \times \{…

Distributing Retractions, Weak Distributive Laws and Applications to Monads of Hyperspaces, Continuous Valuations and Measures
Jean Goubault-Larrecq
https://arxiv.org/abs/2507.18418

Distributing Retractions, Weak Distributive Laws and Applications to Monads of Hyperspaces, Continuous Valuations and Measures
Given two monads $S$, $T$ on a category where idempotents split, and a weak distributive law between them, one can build a combined monad $U$. Making explicit what this monad $U$ is requires some effort. When we already have an idea what $U$ should be, we show how to recognize that $U$ is indeed the combined monad obtained from $S$ and $T$: it suffices to exhibit what we call a distributing retraction of $ST$ onto $U$. We show that distributing retractions and weak distributive laws are in one-…

Constructing and transforming standard resolutions of local modules
Xingbang Hao
https://arxiv.org/abs/2508.11306 https://arxiv.org/pdf/2508.11306

Constructing and transforming standard resolutions of local modules
We construct standard resolutions for analytic local modules on complex hypersurfaces using standard basis methods, with extensions to complete intersections. The algebraic version over arbitrary infinite fields is also suggested. Applications include derived category formula of local hypersurface blow-ups, revealing new connections between standard bases and categorical geometry.

Tilting theory for hypersurface singularities of dimension one
Osamu Iyama, Junyang Liu
https://arxiv.org/abs/2508.12581 https://arxiv.org/pdf/2508.12581…

Tilting theory for hypersurface singularities of dimension one
It was shown by Buchweitz, the first author, and Yamaura that any $\mathbb{N}$-graded commutative Gorenstein ring $R$ of Krull dimension one with $R_0$ a field admits a standard silting object $V$ in the stable category $\underline{\mathrm{CM}\, \!}_0^{\mathbb{Z}}R$. Moreover, they proved that the object $V$ is tilting if and only if the $a$-invariant $a$ is non-negative. In this article, under the additional assumption that $R$ is a hypersurface singularity, we give an explicit description of …

Perfect tilings with the generalised triangle in $k$-graphs
Weichan Liu, Xiangxiang Nie, Donglei Yang, Lin-Peng Zhang
https://arxiv.org/abs/2508.12311 https://

Perfect tilings with the generalised triangle in $k$-graphs
Denote by $T_k$ the generalised triangle, a $k$-uniform hypergraph on vertex set $\{1,2,\dots,2k-1\}$ with three edges $\{1,\dots,k-1,k\}$,$\{1,\dots,k-1,k+1\}$ and $\{k,k+1,\dots,2k-1\}$. Recently, Bowtell, Kathapurkar, Morrison and Mycroft [arXiv: 2505.05606] established the exact minimum codegree threshold for perfect $T_3$-tilings in $3$-graphs. In this paper, we extend their result to all $k \geq 3$, determining the optimal minimum codegree threshold for perfect $T_k$-tilings in $k$-graphs…