Pub Date : 2026-02-01Epub Date: 2026-01-12DOI: 10.1016/j.jpaa.2026.108171
Donald M. Davis , Douglas C. Ravenel , W. Stephen Wilson
We develop tools for computing the connective n-th Morava K-theory of spaces. Starting with a Universal Coefficient Theorem that computes the cohomology version from the homology version, we show that every step in the process of computing one is mirrored in the other and that this can be used to make computations. As our example, we compute the connective n-th Morava K-theory of the second mod p Eilenberg-MacLane space.
{"title":"The connective Morava K-theory of the second mod p Eilenberg-MacLane space","authors":"Donald M. Davis , Douglas C. Ravenel , W. Stephen Wilson","doi":"10.1016/j.jpaa.2026.108171","DOIUrl":"10.1016/j.jpaa.2026.108171","url":null,"abstract":"<div><div>We develop tools for computing the connective n-th Morava K-theory of spaces. Starting with a Universal Coefficient Theorem that computes the cohomology version from the homology version, we show that every step in the process of computing one is mirrored in the other and that this can be used to make computations. As our example, we compute the connective <em>n</em>-th Morava <em>K</em>-theory of the second mod <em>p</em> Eilenberg-MacLane space.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108171"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2026-01-12DOI: 10.1016/j.jpaa.2026.108173
Shengding Sun , Aljaž Zalar
The matrix Fejér-Riesz theorem characterizes positive semidefinite matrix polynomials on the real line. In [28] this was extended to the characterization on arbitrary closed semialgebraic sets by using matrix quadratic modules from real algebraic geometry. In the compact case there is a denominator-free characterization, while in the non-compact case denominators are needed except when K is the whole line, an unbounded interval, a union of two unbounded intervals, and according to a conjecture of [28] also when K is a union of an unbounded interval and a point or a union of two unbounded intervals and a point. In this paper, we confirm this conjecture by solving the truncated matrix-valued moment problem on a union of a bounded interval and a point. The presented technique for solving the corresponding moment problem can potentially be used to determine degree bounds in the positivity certificates for matrix polynomials on compact sets K[28, Theorem C].
{"title":"Matrix Fejér-Riesz type theorem for a union of an interval and a point","authors":"Shengding Sun , Aljaž Zalar","doi":"10.1016/j.jpaa.2026.108173","DOIUrl":"10.1016/j.jpaa.2026.108173","url":null,"abstract":"<div><div>The matrix Fejér-Riesz theorem characterizes positive semidefinite matrix polynomials on the real line. In <span><span>[28]</span></span> this was extended to the characterization on arbitrary closed semialgebraic sets <span><math><mi>K</mi><mo>⊆</mo><mi>R</mi></math></span> by using matrix quadratic modules from real algebraic geometry. In the compact case there is a denominator-free characterization, while in the non-compact case denominators are needed except when <em>K</em> is the whole line, an unbounded interval, a union of two unbounded intervals, and according to a conjecture of <span><span>[28]</span></span> also when <em>K</em> is a union of an unbounded interval and a point or a union of two unbounded intervals and a point. In this paper, we confirm this conjecture by solving the truncated matrix-valued moment problem on a union of a bounded interval and a point. The presented technique for solving the corresponding moment problem can potentially be used to determine degree bounds in the positivity certificates for matrix polynomials on compact sets <em>K</em> <span><span>[28, Theorem C]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108173"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2026-01-27DOI: 10.1016/j.jpaa.2026.108182
Petter Andreas Bergh , David A. Jorgensen , Peder Thompson
Given a graded-commutative ring acting centrally on a triangulated category, our main result shows that if cohomology of a pair of objects of the triangulated category is finitely generated over the ring acting centrally, then the asymptotic vanishing of the cohomology is well-behaved. In particular, enough consecutive asymptotic vanishing of cohomology implies all eventual vanishing. Several key applications are also given.
{"title":"Asymptotic vanishing of cohomology in triangulated categories","authors":"Petter Andreas Bergh , David A. Jorgensen , Peder Thompson","doi":"10.1016/j.jpaa.2026.108182","DOIUrl":"10.1016/j.jpaa.2026.108182","url":null,"abstract":"<div><div>Given a graded-commutative ring acting centrally on a triangulated category, our main result shows that if cohomology of a pair of objects of the triangulated category is finitely generated over the ring acting centrally, then the asymptotic vanishing of the cohomology is well-behaved. In particular, enough consecutive asymptotic vanishing of cohomology implies all eventual vanishing. Several key applications are also given.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108182"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2026-01-08DOI: 10.1016/j.jpaa.2026.108170
J. Reina
This paper establishes a relation between two invariants of 3-dimensional manifolds: the chromatic spherical invariant and the Hennings-Kauffman-Radford invariant HKR. We show that, for a spherical Hopf algebra H, the invariant associated to the pivotal category of finite-dimensional H-modules is equal to the invariant HKR associated to the Drinfeld double of the same Hopf algebra.
{"title":"Chromatic spherical invariant and Hennings invariant of 3-dimensional manifolds","authors":"J. Reina","doi":"10.1016/j.jpaa.2026.108170","DOIUrl":"10.1016/j.jpaa.2026.108170","url":null,"abstract":"<div><div>This paper establishes a relation between two invariants of 3-dimensional manifolds: the chromatic spherical invariant <span><math><mi>K</mi></math></span> and the Hennings-Kauffman-Radford invariant HKR. We show that, for a spherical Hopf algebra <em>H</em>, the invariant <span><math><mi>K</mi></math></span> associated to the pivotal category of finite-dimensional <em>H</em>-modules is equal to the invariant HKR associated to the Drinfeld double <span><math><mi>D</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> of the same Hopf algebra.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108170"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145950134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2026-01-27DOI: 10.1016/j.jpaa.2026.108185
Tomasz Ciborski
The aim of this paper is to calculate entropy in the sense of Dimitrov–Haiden–Katzarkov–Kontsevich and polynomial entropy as defined by Fan–Fu–Ouchi of derived autoequivalences of derived discrete algebras over an algebraically closed field.
{"title":"Entropy and polynomial entropy of derived autoequivalences of derived discrete algebras","authors":"Tomasz Ciborski","doi":"10.1016/j.jpaa.2026.108185","DOIUrl":"10.1016/j.jpaa.2026.108185","url":null,"abstract":"<div><div>The aim of this paper is to calculate entropy in the sense of Dimitrov–Haiden–Katzarkov–Kontsevich and polynomial entropy as defined by Fan–Fu–Ouchi of derived autoequivalences of derived discrete algebras over an algebraically closed field.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108185"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2026-01-27DOI: 10.1016/j.jpaa.2026.108187
Srishti Singh, Hema Srinivasan
Consider a numerical semigroup minimally generated by a subset of the interval with multiplicity e and width . Such numerical semigroups are called Sally type semigroups. We show that the defining ideals of these semigroup rings, when the embedding dimension is , generically have the structure of the sum of two determinantal ideals. More generally, Sally type numerical semigroups with multiplicity e and embedding dimension are obtained by introducing k gaps in the interval . It is known that for , there is precisely one such semigroup that is Gorenstein, and it happens when one deletes consecutive integers. Let denote the Sally type numerical semigroup of multiplcity e, embedding dimension obtained by deleting the k consecutive integers . We prove that for any , the semigroup is Gorenstein if and only if . We construct an explicit minimal free resolution of the semigroup ring of and compute the Betti numbers. In general, we characterize when are symmetric and construct minimal resolutions for these Gorenstein semigroup rings.
{"title":"Structure and symmetry of sally type semigroup rings","authors":"Srishti Singh, Hema Srinivasan","doi":"10.1016/j.jpaa.2026.108187","DOIUrl":"10.1016/j.jpaa.2026.108187","url":null,"abstract":"<div><div>Consider a numerical semigroup minimally generated by a subset of the interval <span><math><mo>[</mo><mi>e</mi><mo>,</mo><mn>2</mn><mi>e</mi><mo>−</mo><mn>1</mn><mo>]</mo></math></span> with multiplicity <em>e</em> and width <span><math><mi>e</mi><mo>−</mo><mn>1</mn></math></span>. Such numerical semigroups are called Sally type semigroups. We show that the defining ideals of these semigroup rings, when the embedding dimension is <span><math><mi>e</mi><mo>−</mo><mn>2</mn></math></span>, generically have the structure of the sum of two determinantal ideals. More generally, Sally type numerical semigroups with multiplicity <em>e</em> and embedding dimension <span><math><mi>d</mi><mo>=</mo><mi>e</mi><mo>−</mo><mi>k</mi></math></span> are obtained by introducing <em>k</em> gaps in the interval <span><math><mo>[</mo><mi>e</mi><mo>,</mo><mn>2</mn><mi>e</mi><mo>−</mo><mn>1</mn><mo>]</mo></math></span>. It is known that for <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span>, there is precisely one such semigroup that is Gorenstein, and it happens when one deletes consecutive integers. Let <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mi>k</mi></mrow><mrow><mi>e</mi></mrow></msubsup><mo>(</mo><mi>j</mi><mo>)</mo></math></span> denote the Sally type numerical semigroup of multiplcity <em>e</em>, embedding dimension <span><math><mi>e</mi><mo>−</mo><mi>k</mi></math></span> obtained by deleting the <em>k</em> consecutive integers <span><math><mi>j</mi><mo>,</mo><mi>j</mi><mo>+</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>j</mi><mo>+</mo><mi>k</mi><mo>−</mo><mn>1</mn></math></span>. We prove that for any <span><math><mn>1</mn><mo>≤</mo><mi>k</mi><mo><</mo><mi>e</mi><mo>/</mo><mn>2</mn></math></span>, the semigroup <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mi>k</mi></mrow><mrow><mi>e</mi></mrow></msubsup><mo>(</mo><mi>j</mi><mo>)</mo></math></span> is Gorenstein if and only if <span><math><mi>j</mi><mo>=</mo><mi>k</mi></math></span>. We construct an explicit minimal free resolution of the semigroup ring of <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mi>k</mi></mrow><mrow><mi>e</mi></mrow></msubsup><mo>(</mo><mi>k</mi><mo>)</mo></math></span> and compute the Betti numbers. In general, we characterize when <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mi>k</mi></mrow><mrow><mi>e</mi></mrow></msubsup><mo>(</mo><mi>j</mi><mo>)</mo></math></span> are symmetric and construct minimal resolutions for these Gorenstein semigroup rings.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108187"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2026-02-04DOI: 10.1016/j.jpaa.2026.108195
Wan Keng Cheong, Ngau Lam
We prove an equivalence between the actions of the Gaudin algebras with irregular singularities for and on the Fock space of bosonic and fermionic oscillators. This establishes a duality of for Gaudin models. As an application, we show that the Gaudin algebra with irregular singularities for acts cyclically on each weight space of a certain class of infinite-dimensional modules over a direct sum of Takiff superalgebras over and that the action is diagonalizable with a simple spectrum under a generic condition. We also study the classical versions of Gaudin algebras with irregular singularities and demonstrate a duality of for classical Gaudin models.
{"title":"Dualities of Gaudin models with irregular singularities for general linear Lie (super)algebras","authors":"Wan Keng Cheong, Ngau Lam","doi":"10.1016/j.jpaa.2026.108195","DOIUrl":"10.1016/j.jpaa.2026.108195","url":null,"abstract":"<div><div>We prove an equivalence between the actions of the Gaudin algebras with irregular singularities for <span><math><msub><mrow><mi>gl</mi></mrow><mrow><mi>d</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>gl</mi></mrow><mrow><mi>p</mi><mo>+</mo><mi>m</mi><mo>|</mo><mi>q</mi><mo>+</mo><mi>n</mi></mrow></msub></math></span> on the Fock space of <span><math><mi>d</mi><mo>(</mo><mi>p</mi><mo>+</mo><mi>m</mi><mo>)</mo></math></span> bosonic and <span><math><mi>d</mi><mo>(</mo><mi>q</mi><mo>+</mo><mi>n</mi><mo>)</mo></math></span> fermionic oscillators. This establishes a duality of <span><math><mo>(</mo><msub><mrow><mi>gl</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>,</mo><msub><mrow><mi>gl</mi></mrow><mrow><mi>p</mi><mo>+</mo><mi>m</mi><mo>|</mo><mi>q</mi><mo>+</mo><mi>n</mi></mrow></msub><mo>)</mo></math></span> for Gaudin models. As an application, we show that the Gaudin algebra with irregular singularities for <span><math><msub><mrow><mi>gl</mi></mrow><mrow><mi>p</mi><mo>+</mo><mi>m</mi><mo>|</mo><mi>q</mi><mo>+</mo><mi>n</mi></mrow></msub></math></span> acts cyclically on each weight space of a certain class of infinite-dimensional modules over a direct sum of Takiff superalgebras over <span><math><msub><mrow><mi>gl</mi></mrow><mrow><mi>p</mi><mo>+</mo><mi>m</mi><mo>|</mo><mi>q</mi><mo>+</mo><mi>n</mi></mrow></msub></math></span> and that the action is diagonalizable with a simple spectrum under a generic condition. We also study the classical versions of Gaudin algebras with irregular singularities and demonstrate a duality of <span><math><mo>(</mo><msub><mrow><mi>gl</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>,</mo><msub><mrow><mi>gl</mi></mrow><mrow><mi>p</mi><mo>+</mo><mi>m</mi><mo>|</mo><mi>q</mi><mo>+</mo><mi>n</mi></mrow></msub><mo>)</mo></math></span> for classical Gaudin models.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108195"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2026-02-04DOI: 10.1016/j.jpaa.2026.108193
Zachary Nason
Let R be a commutative noetherian local differential graded (DG) ring. In this paper we propose a definition of a maximal Cohen-Macaulay DG-complex over R that naturally generalizes a maximal Cohen-Macaulay complex over a noetherian local ring, as studied by Iyengar, Ma, Schwede, and Walker. Our proposed definition extends the work of Shaul on Cohen-Macaulay DG-rings and DG-modules, as any maximal Cohen-Macaulay DG-module is a maximal Cohen-Macaulay DG-complex. After proving necessary lemmas in derived commutative algebra, we establish the existence of a maximal Cohen-Macaulay DG-complex for every DG-ring with constant amplitude that admits a dualizing DG-module. We then use the existence of these DG-complexes to establish a derived Improved New Intersection Theorem for all DG-rings with constant amplitude.
{"title":"Maximal Cohen-Macaulay DG-complexes","authors":"Zachary Nason","doi":"10.1016/j.jpaa.2026.108193","DOIUrl":"10.1016/j.jpaa.2026.108193","url":null,"abstract":"<div><div>Let <em>R</em> be a commutative noetherian local differential graded (DG) ring. In this paper we propose a definition of a maximal Cohen-Macaulay DG-complex over <em>R</em> that naturally generalizes a maximal Cohen-Macaulay complex over a noetherian local ring, as studied by Iyengar, Ma, Schwede, and Walker. Our proposed definition extends the work of Shaul on Cohen-Macaulay DG-rings and DG-modules, as any maximal Cohen-Macaulay DG-module is a maximal Cohen-Macaulay DG-complex. After proving necessary lemmas in derived commutative algebra, we establish the existence of a maximal Cohen-Macaulay DG-complex for every DG-ring with constant amplitude that admits a dualizing DG-module. We then use the existence of these DG-complexes to establish a derived Improved New Intersection Theorem for all DG-rings with constant amplitude.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108193"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2026-01-27DOI: 10.1016/j.jpaa.2026.108184
Enric Nart , Josnei Novacoski
The depth of a simple algebraic extension of valued fields is the minimal length of the Mac Lane-Vaquié chains of the valuations on determined by the choice of different generators of the extension. In [11], we characterized the defectless unibranched extensions of depth one. In this paper, we analyze this problem for towers of Artin-Schreier defect extensions. Under certain conditions on , we prove that the towers obtained as the compositum of linearly disjoint defect Artin-Schreier extensions of K have depth one. We conjecture that these are the only depth one Artin-Schreier defect towers and we present some examples supporting this conjecture.
有值域的简单代数扩展（L/K,v）的深度是K[x]上的赋值的Mac lane - vaqui链的最小长度，该长度由该扩展的不同生成器的选择决定。在[11]中，我们刻画了深度1的无缺陷无分支扩展。本文分析了Artin-Schreier缺陷扩展塔的这一问题。在（K,v）上的一定条件下，证明了由K的线性不相交缺陷Artin-Schreier扩展复合得到的塔深度为1。我们推测这些是唯一深度的阿汀-施赖尔缺陷塔，我们提出了一些例子来支持这一猜想。
{"title":"Depth of Artin-Schreier defect towers","authors":"Enric Nart , Josnei Novacoski","doi":"10.1016/j.jpaa.2026.108184","DOIUrl":"10.1016/j.jpaa.2026.108184","url":null,"abstract":"<div><div>The depth of a simple algebraic extension <span><math><mo>(</mo><mi>L</mi><mo>/</mo><mi>K</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></span> of valued fields is the minimal length of the Mac Lane-Vaquié chains of the valuations on <span><math><mi>K</mi><mo>[</mo><mi>x</mi><mo>]</mo></math></span> determined by the choice of different generators of the extension. In <span><span>[11]</span></span>, we characterized the defectless unibranched extensions of depth one. In this paper, we analyze this problem for towers of Artin-Schreier defect extensions. Under certain conditions on <span><math><mo>(</mo><mi>K</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></span>, we prove that the towers obtained as the compositum of linearly disjoint defect Artin-Schreier extensions of <em>K</em> have depth one. We conjecture that these are the only depth one Artin-Schreier defect towers and we present some examples supporting this conjecture.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 2","pages":"Article 108184"},"PeriodicalIF":0.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-01Epub Date: 2025-12-15DOI: 10.1016/j.jpaa.2025.108165
Clémence Chanavat, Amar Hadzihasanovic
We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict ω- categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the expected properties: they include all degenerate cells, are closed under 2-out-of-3, and satisfy an appropriate version of the “division lemma”, which ensures that enwrapping a diagram with equivalences at all sides is an invertible operation up to higher equivalence. On the way to this result, we develop methods, such as an algebraic calculus of natural equivalences, for handling the weak units and unitors which set this framework apart from strict ω- categories.
{"title":"Equivalences in diagrammatic sets","authors":"Clémence Chanavat, Amar Hadzihasanovic","doi":"10.1016/j.jpaa.2025.108165","DOIUrl":"10.1016/j.jpaa.2025.108165","url":null,"abstract":"<div><div>We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict <em>ω</em>-<!--> <!-->categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the expected properties: they include all degenerate cells, are closed under 2-out-of-3, and satisfy an appropriate version of the “division lemma”, which ensures that enwrapping a diagram with equivalences at all sides is an invertible operation up to higher equivalence. On the way to this result, we develop methods, such as an algebraic calculus of natural equivalences, for handling the weak units and unitors which set this framework apart from strict <em>ω</em>-<!--> <!-->categories.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 1","pages":"Article 108165"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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