Tootfinder

Really important practical question: how to do type search for #Agda.
Unification Modulo Isomorphisms between Dependent Types for Type-based Library Search
Presented by Satoshi Takimoto. Joint work with Sosuke Moriguchi, Takuo Watanabe

A note on adding isomorphisms and the pseudointersection number
Corey Bacal Switzer
https://arxiv.org/abs/2510.11155 https://arxiv.org/pdf/2510.11155

A note on adding isomorphisms and the pseudointersection number
We prove that for every tower $\mathcal T$ there are $\aleph_1$-dense $A$ and $B$ so that any ``reasonable" forcing notion $\mathbb{P}$ -- an adjective that includes all known ones -- for making $A$ and $B$ isomorphic will add a pseudointersection for the tower. This shows in particular that $\mathsf{MA}_{\aleph_1}(σ{\rm -centered})$ holds in all known models of $\mathsf{BA}$, which provides intrigue to well known questions of Todorčević and Steprāns-Watson.

Asymptotically rigid mapping class groups III: Presentations and isomorphisms
Anthony Genevois, Anne Lonjou, Christian Urech
https://arxiv.org/abs/2510.11336 https://

Asymptotically rigid mapping class groups III: Presentations and isomorphisms
This article is dedicated to the computation of an explicit presentation of some asymptotically rigid mapping class groups, namely the braided Higman-Thompson groups. To do so, we use the action of these groups on the spine complex, a simply connected cube complex constructed by the authors in a previous work. In particular, this allows to compute the abelianisations of these groups. With these new algebraic invariants we can handle many new cases of the isomorphism problem for asymptotically r…

Geometry of tropical mutation surfaces with a single mutation
Tomoki Oda
https://arxiv.org/abs/2510.11991 https://arxiv.org/pdf/2510.11991

Geometry of tropical mutation surfaces with a single mutation
Recently, Escobar, Harada, and Manon introduced the theory of polyptych lattices. This theory gives a general framework for constructing projective varieties from polytopes in a polyptych lattice. When all the mutations of the polyptych lattice are linear isomorphisms, this framework recovers the classical theory of toric varieties. In this article, we study rank two polyptych lattices with a single mutation. We prove that the associated projective surface $X$ is a $\mathbb{G}_m$-surface that a…

Geometry of dyadic polygons II: isomorphisms of dyadic triangles
A. Mu\'cka, A. B. Romanowska
https://arxiv.org/abs/2510.07244 https://arxiv.org/pdf/25…

Geometry of dyadic polygons II: isomorphisms of dyadic triangles
This paper is the second part of a two-part paper investigating the structure and properties of dyadic polygons. A dyadic polygon is the intersection of the dyadic subplane $D^2$ of the real plane $R^2$ and a real convex polygon with vertices in the dyadic plane. Such polygons are described as subreducts (subalgebras of reducts) of the affine dyadic plane $D^2$, or equivalently as commutative, entropic and idempotent groupoids under the binary operation of arithmetic mean. The first part of the…

Relative Gieseker's problem on $F$-divided bundles
Adrian Langer
https://arxiv.org/abs/2510.10583 https://arxiv.org/pdf/2510.10583

Relative Gieseker's problem on $F$-divided bundles
Let $f: X\to Y$ be a surjective morphism of normal projective varieties defined over an algebraically closed field of positive characteristic. We prove that if the induced map on étale fundamental groups is surjective then the corresponding map on $F$-divided fundamental groups is faithfully flat. We also prove an analogous result for isomorphisms. This generalizes and strengthens a recent result of X. Sun and L. Zhang \cite{Sun-Zhang2025}, which in turn generalized earlier results of H. Esnau…

Isomorphisms, Moduli, and Cohomological Dimension for Twisted Triangular Banach Algebras
Sara Behnamian, Fatemeh Fogh
https://arxiv.org/abs/2510.03806 https://

Isomorphisms, Moduli, and Cohomological Dimension for Twisted Triangular Banach Algebras
We introduce and study twisted triangular Banach algebras T_sigma(A,B;X), built from Banach algebras A,B, a Banach A-B bimodule X, and a pair of automorphisms sigma=(sigma_A,sigma_B). This construction extends the classical triangular framework by incorporating twisted module actions on the off-diagonal block. We obtain a complete isomorphism classification: T_sigma is isomorphic to T_tau precisely when the diagonal twists are conjugate, the bimodule admits an (alpha,beta)-equivariant isomorphi…

On isomorphisms between quiver Yangians
Vishnu Jejjala, Dumisani Nxumalo, Konstantinos Zoubos
https://arxiv.org/abs/2509.19288 https://arxiv.org/pdf/2509.1…

The commutative algebra of congruence ideals and applications to number theory
Srikanth B. Iyengar, Chandrashekhar B. Khare, Jeffrey Manning
https://arxiv.org/abs/2510.05418 htt…

The commutative algebra of congruence ideals and applications to number theory
In his proof of Fermat's Last Theorem, Wiles deployed a commutative algebra technique, namely a numerical criterion for detecting isomorphisms of rings. In our recent work we pick up on Wiles' work and generalize the numerical criterion to ``higher codimension''. A critical ingredient is a notion of congruence module in higher codimension: this has turned out to be a key definition whose utility extends beyond the role it plays in the numerical criterion. In this paper we trace the origin of so…

Functor-induced isomorphisms and $G$-matrices
Shengfei Geng
https://arxiv.org/abs/2509.17781 https://arxiv.org/pdf/2509.17781

Functor-induced isomorphisms and $G$-matrices
In this paper, we explore how functor-induced isomorphisms are encoded by $G$-matrices. We first show that the Grothendieck group isomorphism induced by a tilting module can be realized via the $G$-matrix of this tilting module. Building on this, we compare $g$-vectors for a tilted algebra and its associated hereditary algebra, and provide $G$-matrix interpretations of the Coxeter transformation, the Nakayama functor, and the Auslander-Reiten translation for suitable algebras. Furthermore, we d…

On global isomorphisms and a closure property of semigroups
Lingxi Li, Salvatore Tringali
https://arxiv.org/abs/2510.00772 https://arxiv.org/pdf/2510.00772…

On global isomorphisms and a closure property of semigroups
Let $S$ be a semigroup (written multiplicatively). Endowed with the operation of setwise multiplication induced by $S$ on its parts, the non-empty subsets of $S$ form themselves a semigroup, denoted by $\mathcal P(S)$. Accordingly, we say that a semigroup $H$ is globally isomorphic to a semigroup $K$ if $\mathcal P(H)$ is isomorphic to $\mathcal P(K)$; and that a class $\mathscr C$ of semigroups is globally closed if a semigroup in $\mathscr C$ can only be globally isomorphic to an isomorphic c…

Ortho-isomorphisms of von Neumann algebras
Minghui Ma, Weijuan Shi
https://arxiv.org/abs/2509.14697 https://arxiv.org/pdf/2509.14697

Ortho-isomorphisms of von Neumann algebras
Suppose $\mathscr M$ and $\mathscr N$ are von Neumann algebras. Two operators $A$ and $B$ in $\mathscr M$ are said to be orthogonal if $A^*B=0$, meaning their ranges are orthogonal. Let $φ\colon\mathscr M\to\mathscr N$ be a map. We say that $φ$ is an ortho-isomorphism if it is bijective and satisfies that $A^*B=0$ if and only if $φ(A)^*φ(B)=0$ for all $A,B\in\mathscr M$. The map $φ$ is called ortho-additive if the additive relation $φ(A+B)=φ(A)+φ(B)$ holds for all $A,B\in \mathscr M$ wi…

Replaced article(s) found for cs.LO. https://arxiv.org/list/cs.LO/new
[1/1]:
- Type Isomorphisms for Multiplicative-Additive Linear Logic
R\'emi Di Guardia (LIP, PLUME), Olivier Laurent (LIP, PLUME)

Goldman-Turaev formality from the Kontsevitch integral
Dror Bar-Natan, Zsuzsanna Dancso, Tamara Hogan, Jessica Liu, Nancy Scherich
https://arxiv.org/abs/2509.20983 https://

Goldman-Turaev formality from the Kontsevitch integral
We present a new solution to the formality problem for the framed Goldman--Turaev Lie bialgebra, constructing Goldman-Turaev homomorphic expansions (formality isomorphisms) from the Kontsevich integral. Our proof uses a three dimensional derivation of the Goldman-Turaev Lie biaglebra arising from a low-degree Vassiliev quotient -- the {\em emergent} quotient -- of tangles in a thickened punctured disk, modulo a Conway skein relation. This is in contrast to Massuyeau's 2018 proof using braids. A…

Adhesive category theory for graph rewriting in Rocq
Samuel Arsac (PLUME, LIP, ENS de Lyon), Russ Harmer (PLUME, LIP), Damien Pous (PLUME, LIP)
https://arxiv.org/abs/2509.17392 …

Adhesive category theory for graph rewriting in Rocq
We design a Rocq library about adhesive categories, using Hierarchy Builder (HB). It is built around two hierarchies. The first is for categories, with usual categories at the bottom and adhesive categories at the top, with weaker variants of adhesive categories in between. The second is for morphisms (notably isomorphisms, monomorphisms and regular monomorphisms). Each level of these hierarchies is equipped with several interfaces to define instances. We cover basic categorical concepts such a…

Symplectic criteria for elliptic curves, revisited
Alain Kraus, Nuno Freitas, Ignasi S\'anchez-Rodr\'iguez
https://arxiv.org/abs/2509.19938 https://

Symplectic criteria for elliptic curves, revisited
Let $\ell$ and $p \geq 3$ be different primes. Let $E/\mathbb{Q}_\ell$ and $E'/\mathbb{Q}_\ell$ be elliptic curves with isomorphic $p$-torsion. Assume that $E$ has potentially multiplicative reduction. We classify when all $G_{\mathbb{Q}_\ell}$-isomorphisms $ϕ: E[p] \to E'[p]$ have the same symplectic type and prove two new criteria to determine the type in that case. In particular, when both curves have multiplicative reduction, our results cover the case of unramified $p$-torsion which is no…

$c$-structures and trace methods beyond connective rings
Ishan Levy, Vladimir Sosnilo
https://arxiv.org/abs/2509.14774 https://arxiv.org/pdf/2509.14774

$c$-structures and trace methods beyond connective rings
We introduce the notion of a $c$-category, which is a kind of category whose behaviour is controlled by connective ring spectra. More precisely, any $c$-category admits a finite step resolution by categories of compact modules over connective ring spectra. We introduce nilpotent extensions of $c$-categories, and show that they induce isomorphisms on truncating invariants, such as the fiber of the cyclotomic trace map. We show that for many stacks, the category of perfect complexes is naturally …

Ecalle's senary relation and dimorphic structures
Hanamichi Kawamura
https://arxiv.org/abs/2509.21252 https://arxiv.org/pdf/2509.21252

Ecalle's senary relation and dimorphic structures
This paper gives a completed proof of Ecalle's senary relation in the original form. As an application, we obtain another proof of the fact that the double shuffle Lie algebra injects into the Kashiwara--Vergne Lie algebra. We also give two explicit isomorphisms between some dimorphic Lie algebras and their linearized version.