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MATHEMATICS (714 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 4)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 29)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 10)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 3)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 19)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 13)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 3)
Advances in Materials Science     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 4)
Advances in Mathematics     Full-text available via subscription   (Followers: 11)
Advances in Numerical Analysis     Open Access   (Followers: 5)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 6)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 6)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 5)
Analysis Mathematica     Full-text available via subscription  
Analysis. International mathematical journal of analysis and its applications     Hybrid Journal   (Followers: 2)
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 4)
Annals of Data Science     Hybrid Journal   (Followers: 12)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription   (Followers: 1)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 3)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 2)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 20)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 12)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 19)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 29)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Combinatorics     Open Access  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 4)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  

        1 2 3 4 | Last

Journal Cover
Applied Categorical Structures
Journal Prestige (SJR): 0.49
Number of Followers: 2  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1572-9095 - ISSN (Online) 0927-2852
Published by Springer-Verlag Homepage  [2348 journals]
  • Maximal Ideals in Module Categories and Applications
    • Authors: Manuel Cortés-Izurdiaga; Alberto Facchini
      Pages: 617 - 629
      Abstract: We study the existence of maximal ideals in preadditive categories defining an order \(\preceq \) between objects, in such a way that if there do not exist maximal objects with respect to \(\preceq \) , then there is no maximal ideal in the category. In our study, it is sometimes sufficient to restrict our attention to suitable subcategories. We give an example of a category \(\mathbf {C}_F\) of modules over a right noetherian ring R in which there is a unique maximal ideal. The category \(\mathbf {C}_F\) is related to an indecomposable injective module F, and the objects of \(\mathbf {C}_F\) are the R-modules of finite F-rank.
      PubDate: 2018-08-01
      DOI: 10.1007/s10485-017-9505-z
      Issue No: Vol. 26, No. 4 (2018)
  • Open Maps of Involutive Quantales
    • Authors: Pedro Resende
      Pages: 631 - 644
      Abstract: By a map \(p:Q\rightarrow X\) of involutive quantales is meant a homomorphism \(p^*:X\rightarrow Q\) . Calling a map p weakly open if \(p^*\) has a left adjoint \(p_!\) which satisfies the Frobenius reciprocity condition (i.e., \(p_!\) is a homomorphism of X-modules), we say that p is open if it is stably weakly open. We also study a two-sided version, FR2, of the Frobenius reciprocity condition, and show that the weakly open surjections that satisfy FR2 are open. Maps of the latter kind arise in the study of Fell bundles on groupoids.
      PubDate: 2018-08-01
      DOI: 10.1007/s10485-017-9506-y
      Issue No: Vol. 26, No. 4 (2018)
  • Strictly Zero-Dimensional Biframes and a Characterisation of Congruence
    • Authors: Graham Manuell
      Pages: 645 - 655
      Abstract: Strictly zero-dimensional biframes were introduced by Banaschewski and Brümmer as a class of strongly zero-dimensional biframes including the congruence biframes. We consider the category of strictly zero-dimensional biframes and show it is both complete and cocomplete. We characterise the extremal epimorphisms in this category and explore the special position that congruence biframes hold in it. Finally, we provide an internal characterisation of congruence biframes, and hence, of congruence frames.
      PubDate: 2018-08-01
      DOI: 10.1007/s10485-017-9507-x
      Issue No: Vol. 26, No. 4 (2018)
  • Ladders of Compactly Generated Triangulated Categories and Preprojective
    • Authors: Nan Gao; Chrysostomos Psaroudakis
      Pages: 657 - 679
      Abstract: In this paper we characterize when a recollement of compactly generated triangulated categories admits a ladder of some height going either upwards or downwards. As an application, we show that the derived category of the preprojective algebra of Dynkin type \(\mathbb {A}_n\) admits a periodic infinite ladder, where the one outer term in the recollement is the derived category of a differential graded algebra.
      PubDate: 2018-08-01
      DOI: 10.1007/s10485-017-9508-9
      Issue No: Vol. 26, No. 4 (2018)
  • Rickart and Dual Rickart Objects in Abelian Categories: Transfer via
    • Authors: Septimiu Crivei; Gabriela Olteanu
      Pages: 681 - 698
      Abstract: We study the transfer of (dual) relative Rickart properties via functors between abelian categories, and we deduce the transfer of (dual) relative Baer property. We also give applications to Grothendieck categories, comodule categories and (graded) module categories, with emphasis on endomorphism rings.
      PubDate: 2018-08-01
      DOI: 10.1007/s10485-017-9509-8
      Issue No: Vol. 26, No. 4 (2018)
  • Approximate Injectivity
    • Authors: J. Rosický; W. Tholen
      Pages: 699 - 716
      Abstract: In a locally \(\lambda \) -presentable category, with \(\lambda \) a regular cardinal, classes of objects that are injective with respect to a family of morphisms whose domains and codomains are \(\lambda \) -presentable, are known to be characterized by their closure under products, \(\lambda \) -directed colimits and \(\lambda \) -pure subobjects. Replacing the strict commutativity of diagrams by “commutativity up to \(\mathcal {\varepsilon }\) ”, this paper provides an “approximate version” of this characterization for categories enriched over metric spaces. It entails a detailed discussion of the needed \(\mathcal {\varepsilon }\) -generalizations of the notion of \(\lambda \) -purity. The categorical theory is being applied to the locally \(\aleph _1\) -presentable category of Banach spaces and their linear operators of norm at most 1, culminating in a largely categorical proof for the existence of the so-called Gurarii Banach space.
      PubDate: 2018-08-01
      DOI: 10.1007/s10485-017-9510-2
      Issue No: Vol. 26, No. 4 (2018)
  • Grothendieck Categories as a Bilocalization of Linear Sites
    • Authors: Julia Ramos González
      Pages: 717 - 745
      Abstract: Let k be a commutative ring. We prove that the 2-category \(\mathsf {Grt}_k\) of Grothendieck abelian k-linear categories with colimit preserving k-linear functors and k-linear natural transformations is a bicategory of fractions in the sense of Pronk [17] of the 2-category \(\mathsf {Site}_{k,\mathsf {cont}}\) of k-linear sites with k-linear continuous functors and k-linear natural transformations. In complete analogy, we prove that the conjugate-opposite 2-category of the 2-category \(\mathsf {Topoi}_k\) of Grothendieck abelian k-linear categories with k-linear geometric morphisms and k-linear morphisms between them is a bicategory of fractions of the 2-category \(\mathsf {Site}_k\) of k-linear sites with k-linear morphisms of sites and k-linear natural transformations. In addition, we show how the first statement can potentially be used to make the tensor product of Grothendieck categories from [14] into a bi-monoidal structure on \(\mathsf {Grt}_k\) .
      PubDate: 2018-08-01
      DOI: 10.1007/s10485-017-9511-1
      Issue No: Vol. 26, No. 4 (2018)
  • Extensions of Operators, Liftings of Monads, and Distributive Laws
    • Authors: Shilong Zhang; Li Guo; William Keigher
      Pages: 747 - 765
      Abstract: In a previous study, the algebraic formulation of the First Fundamental Theorem of Calculus (FFTC) is shown to allow extensions of differential and Rota–Baxter operators on the one hand, and to give rise to categorical explanations using the ideas of liftings of monads and comonads, and mixed distributive laws on the other. Generalizing the FFTC, we consider in this paper a class of constraints between a differential operator and a Rota–Baxter operator. For a given constraint, we show that the existences of extensions of differential and Rota–Baxter operators, of liftings of monads and comonads, and of mixed distributive laws are equivalent.
      PubDate: 2018-08-01
      DOI: 10.1007/s10485-018-9517-3
      Issue No: Vol. 26, No. 4 (2018)
  • A Synthetic Version of Lie’s Second Theorem
    • Authors: Matthew Burke
      Pages: 767 - 798
      Abstract: We formulate and prove a generalisation of Lie’s second theorem that integrates homomorphisms between formal group laws to homomorphisms between Lie groups. Firstly we generalise classical Lie theory by replacing groups with groupoids. Secondly we include groupoids whose underlying spaces are not smooth manifolds. The main intended application is when we replace the category of smooth manifolds with a well-adapted model of synthetic differential geometry. In addition we provide an axiomatic system that provides all the abstract structure that is required to prove Lie’s second theorem.
      PubDate: 2018-08-01
      DOI: 10.1007/s10485-018-9518-2
      Issue No: Vol. 26, No. 4 (2018)
  • Fraïssé Limits in Comma Categories
    • Authors: Christian Pech; Maja Pech
      Pages: 799 - 820
      Abstract: Fraïssé’s theorem characterizing the existence of universal homogeneous structures is a cornerstone of model theory. A categorical version of these results was developed by Droste and Göbel. Such an abstract version of Fraïssé theory allows to construct unusual objects that are far away from the usual structures. In this paper we are going to derive sufficient conditions for a comma category to contain universal homogeneous objects. Using this criterion, we characterize homogeneous structures that possess universal homogeneous endomorphisms. The existence of such endomorphisms helps to reduce questions about the full endomorphism monoid to the self-embedding monoid of the structure. As another application we characterize the retracts of homogeneous structures that are induced by universal homogeneous retractions. This extends previous results by Bonato, Delić, Mudrinski, Dolinka, and Kubiś.
      PubDate: 2018-08-01
      DOI: 10.1007/s10485-018-9519-1
      Issue No: Vol. 26, No. 4 (2018)
  • On the Maps of Pointfree Topology Which Preserve the Rings of
           Integervalued Continuous Functions
    • Authors: B. Banaschewski
      Pages: 477 - 489
      Abstract: This paper establishes various conditions characterizing the homomorphisms \(h: L \rightarrow M\) of 0-dimensional frames which induce an isomorphism between the rings of all integervalued continuous function, or their bounded parts, on L and M, based on the Lindelöf and the compact coreflection of 0-dimensional frames. This provides natural analogues of familiar results concerning the realvalued continuous functions on completely regular frames, albeit by rather different methods of proof from those originally used in that setting. In addition, it will be shown that the present approach also leads to alternative proofs for the latter.
      PubDate: 2018-06-01
      DOI: 10.1007/s10485-017-9499-6
      Issue No: Vol. 26, No. 3 (2018)
  • Crossed Simplicial Group Categorical Nerves
    • Authors: Scott Balchin
      Pages: 545 - 558
      Abstract: We extend the notion of the nerve of a category for a small class of crossed simplicial groups, explicitly describing them using generators and relations. We do this by first considering a generalised bar construction of a group before looking at twisted versions of some of these nerves. As an application we show how we can use the twisted nerves to give equivariant versions of certain derived stacks.
      PubDate: 2018-06-01
      DOI: 10.1007/s10485-017-9502-2
      Issue No: Vol. 26, No. 3 (2018)
  • Bousfield Localisation and Colocalisation of One-Dimensional Model
    • Authors: Scott Balchin; Richard Garner
      Abstract: We give an account of Bousfield localisation and colocalisation for one-dimensional model categories—ones enriched over the model category of 0-types. A distinguishing feature of our treatment is that it builds localisations and colocalisations using only the constructions of projective and injective transfer of model structures along right and left adjoint functors, and without any reference to Smith’s theorem.
      PubDate: 2018-08-10
      DOI: 10.1007/s10485-018-9537-z
  • A Multiplication Formula for the Modified Caldero–Chapoton Map
    • Authors: David Pescod
      Abstract: A frieze in the modern sense is a map from the set of objects of a triangulated category \(\mathsf {C}\) to some ring. A frieze X is characterised by the property that if \(\tau x\rightarrow y\rightarrow x\) is an Auslander–Reiten triangle in \(\mathsf {C}\) , then \(X(\tau x)X(x)-X(y)=1\) . The canonical example of a frieze is the (original) Caldero–Chapoton map, which send objects of cluster categories to elements of cluster algebras. Holm and Jørgensen (Nagoya Math J 218:101–124, 2015; Bull Sci Math 140:112–131, 2016), the notion of generalised friezes is introduced. A generalised frieze \(X'\) has the more general property that \(X'(\tau x)X'(x)-X'(y)\in \{0,1\}\) . The canonical example of a generalised frieze is the modified Caldero–Chapoton map, also introduced in Holm and Jørgensen (2015, 2016). Here, we develop and add to the results in Holm and Jørgensen (2016). We define Condition F for two maps \(\alpha \) and \(\beta \) in the modified Caldero–Chapoton map, and in the case when \(\mathsf {C}\) is 2-Calabi–Yau, we show that it is sufficient to replace a more technical “frieze-like” condition from Holm and Jørgensen (2016). We also prove a multiplication formula for the modified Caldero–Chapoton map, which significantly simplifies its computation in practice.
      PubDate: 2018-08-09
      DOI: 10.1007/s10485-018-9538-y
  • Categories of Locally Hypercompact Spaces and Quasicontinuous Posets
    • Authors: Marcel Erné
      Abstract: A subset of a topological space is hypercompact if its saturation (the intersection of its neighborhoods) is generated by a finite set. Locally hypercompact spaces are defined by the existence of hypercompact neighborhood bases at each point. We exhibit many useful properties of such spaces, often based on Rudin’s Lemma, which is equivalent to the Ultrafilter Principle and ensures that the Scott spaces of quasicontinuous domains are exactly the locally hypercompact sober spaces. We characterize their patch spaces (the Lawson spaces) as hyperconvex and hyperregular pospaces in which every monotone net has a supremum to which it converges. Moreover, we find extensions to the non-sober case by replacing suprema with cuts, and we provide topological generalizations of known facts for quasicontinuous posets. Similar results are obtained for hypercompactly based spaces and quasialgebraic posets. Furthermore, locally hypercompact spaces are described by certain relations between finite sets and points, providing a quasiuniform approach to such spaces. Our results lead to diverse old and new equivalences and dualities for categories of locally hypercompact spaces or quasicontinuous posets.
      PubDate: 2018-08-09
      DOI: 10.1007/s10485-018-9536-0
  • Categorical Bockstein Sequences
    • Authors: Leonid Positselski
      Abstract: We construct the reduction of an exact category with a twist functor with respect to an element of its graded center in presence of an exact-conservative forgetful functor annihilating this central element. The construction uses matrix factorizations in a nontraditional way. We obtain the Bockstein long exact sequences for the Ext groups in the exact categories produced by reduction. Our motivation comes from the theory of Artin–Tate motives and motivic sheaves with finite coefficients, and our key techniques generalize those of Positselski (Mosc Math J 11(2):317–402, 2011. arXiv:1006.4343 [math.KT], Section 4).
      PubDate: 2018-07-09
      DOI: 10.1007/s10485-018-9534-2
  • Local Complete Segal Spaces
    • Authors: Nicholas J. Meadows
      Abstract: We develop a model structure on bimplicial presheaves on a small site \({\mathscr {C}}\) , for which the weak equivalences are local (or stalkwise) weak equivalences in the complete Segal model structure. We call this the local Complete Segal model structure. This model structure can be realized as a left Bousfield localization of the Jardine (injective) model structure on the simplicial presheaves on a site \({\mathscr {C}} / {\varDelta }^{op}\) . Furthermore, it is shown that this model structure is Quillen equivalent to the model structure of the author’s paper (Meadows in TAC 31(24):690–711, 2016). This Quillen equivalence extends an equivalence between the complete Segal space and Joyal model structures, due to Joyal and Tierney (Categories in algebra, geometry and mathematical physics, contemporary mathematics, vol. 431. American Mathematical Society, Providence, pp 277–326, 2007). As an application, we compare the notion of descent in the local Joyal model structure to the notion of descent in the injective model structure. Interestingly, this is a consequence of the Quillen equivalence between the local Joyal and local Complete Segal model structures.
      PubDate: 2018-07-07
      DOI: 10.1007/s10485-018-9535-1
  • Correction to: The Other Closure and Complete Sublocales
    • Authors: Maria Manuel Clementino; Jorge Picado; Aleš Pultr
      Abstract: In the original publication of the article, the formulation of the c-subfitness condition (c-sfit) in Subsection 5.2 is inaccurate, with effect in Theorem 5.3.
      PubDate: 2018-06-29
      DOI: 10.1007/s10485-018-9533-3
  • Normality, Regularity and Contractive Realvalued Maps
    • Authors: E. Colebunders; M. Sioen; W. Van Den Haute
      Abstract: For approach spaces normality has been studied from different angles. One way of dealing with it is by focussing on separation by realvalued contractive maps or, equivalently, on Katětov–Tong’s insertion. We call this notion approach normality. Another point of view is using the isomorphism between the category \(\textsf {App}\) of approach spaces and contractions and the category of lax algebras for the ultrafilter monad and the quantale \(\textsf {P}_{\!\!{_+}}\) and applying the monoidal definition of normality. We call this notion monoidal normality. Although both normality properties coincide for topological approach spaces, a comparison of both notions for \(\textsf {App}\) is an open question. In this paper we present a partial solution to this problem. We show that in \(\textsf {App}\) approach normality implies monoidal normality and that both notions coincide on the subcategory of quasimetric approach spaces. Moreover we investigate the relation between approach normality and regularity. Among other things we prove that approach spaces that are approach normal and regular are uniform.
      PubDate: 2018-06-21
      DOI: 10.1007/s10485-018-9532-4
  • Commutativity in Double Interchange Semigroups
    • Authors: Fatemeh Bagherzadeh; Murray Bremner
      Abstract: We extend the work of Kock (J Homot Relat Struct 2(2):217–228, 2007) and Bremner and Madariaga (Semigroup Forum 92:335–360,  2016) on commutativity in double interchange semigroups (DIS) to relations with 10 arguments. Our methods involve the free symmetric operad generated by two binary operations with no symmetry, its quotient by the two associative laws, its quotient by the interchange law, and its quotient by all three laws. We also consider the geometric realization of free double interchange magmas by rectangular partitions of the unit square \(I^2\) . We define morphisms between these operads which allow us to represent elements of free DIS both algebraically as tree monomials and geometrically as rectangular partitions. With these morphisms we reason diagrammatically about free DIS and prove our new commutativity relations.
      PubDate: 2018-06-20
      DOI: 10.1007/s10485-018-9531-5
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