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  Subjects -> STATISTICS (Total: 130 journals)
Showing 1 - 151 of 151 Journals sorted alphabetically
Advances in Complex Systems     Hybrid Journal   (Followers: 11)
Advances in Data Analysis and Classification     Hybrid Journal   (Followers: 62)
Annals of Applied Statistics     Full-text available via subscription   (Followers: 39)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Argumentation et analyse du discours     Open Access   (Followers: 11)
Asian Journal of Mathematics & Statistics     Open Access   (Followers: 8)
AStA Advances in Statistical Analysis     Hybrid Journal   (Followers: 4)
Australian & New Zealand Journal of Statistics     Hybrid Journal   (Followers: 13)
Bernoulli     Full-text available via subscription   (Followers: 9)
Biometrical Journal     Hybrid Journal   (Followers: 11)
Biometrics     Hybrid Journal   (Followers: 52)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 18)
Building Simulation     Hybrid Journal   (Followers: 2)
Bulletin of Statistics     Full-text available via subscription   (Followers: 4)
CHANCE     Hybrid Journal   (Followers: 5)
Communications in Statistics - Simulation and Computation     Hybrid Journal   (Followers: 9)
Communications in Statistics - Theory and Methods     Hybrid Journal   (Followers: 11)
Computational Statistics     Hybrid Journal   (Followers: 14)
Computational Statistics & Data Analysis     Hybrid Journal   (Followers: 37)
Current Research in Biostatistics     Open Access   (Followers: 8)
Decisions in Economics and Finance     Hybrid Journal   (Followers: 11)
Demographic Research     Open Access   (Followers: 15)
Electronic Journal of Statistics     Open Access   (Followers: 8)
Engineering With Computers     Hybrid Journal   (Followers: 5)
Environmental and Ecological Statistics     Hybrid Journal   (Followers: 7)
ESAIM: Probability and Statistics     Full-text available via subscription   (Followers: 5)
Extremes     Hybrid Journal   (Followers: 2)
Fuzzy Optimization and Decision Making     Hybrid Journal   (Followers: 9)
Geneva Papers on Risk and Insurance - Issues and Practice     Hybrid Journal   (Followers: 13)
Handbook of Numerical Analysis     Full-text available via subscription   (Followers: 5)
Handbook of Statistics     Full-text available via subscription   (Followers: 7)
IEA World Energy Statistics and Balances -     Full-text available via subscription   (Followers: 2)
International Journal of Computational Economics and Econometrics     Hybrid Journal   (Followers: 6)
International Journal of Quality, Statistics, and Reliability     Open Access   (Followers: 17)
International Journal of Stochastic Analysis     Open Access   (Followers: 3)
International Statistical Review     Hybrid Journal   (Followers: 13)
International Trade by Commodity Statistics - Statistiques du commerce international par produit     Full-text available via subscription  
Journal of Algebraic Combinatorics     Hybrid Journal   (Followers: 4)
Journal of Applied Statistics     Hybrid Journal   (Followers: 21)
Journal of Biopharmaceutical Statistics     Hybrid Journal   (Followers: 21)
Journal of Business & Economic Statistics     Full-text available via subscription   (Followers: 39, SJR: 3.664, CiteScore: 2)
Journal of Combinatorial Optimization     Hybrid Journal   (Followers: 7)
Journal of Computational & Graphical Statistics     Full-text available via subscription   (Followers: 20)
Journal of Econometrics     Hybrid Journal   (Followers: 84)
Journal of Educational and Behavioral Statistics     Hybrid Journal   (Followers: 6)
Journal of Forecasting     Hybrid Journal   (Followers: 17)
Journal of Global Optimization     Hybrid Journal   (Followers: 7)
Journal of Interactive Marketing     Hybrid Journal   (Followers: 10)
Journal of Mathematics and Statistics     Open Access   (Followers: 8)
Journal of Nonparametric Statistics     Hybrid Journal   (Followers: 6)
Journal of Probability and Statistics     Open Access   (Followers: 10)
Journal of Risk and Uncertainty     Hybrid Journal   (Followers: 33)
Journal of Statistical and Econometric Methods     Open Access   (Followers: 5)
Journal of Statistical Physics     Hybrid Journal   (Followers: 13)
Journal of Statistical Planning and Inference     Hybrid Journal   (Followers: 8)
Journal of Statistical Software     Open Access   (Followers: 21, SJR: 13.802, CiteScore: 16)
Journal of the American Statistical Association     Full-text available via subscription   (Followers: 72, SJR: 3.746, CiteScore: 2)
Journal of the Korean Statistical Society     Hybrid Journal   (Followers: 1)
Journal of the Royal Statistical Society Series C (Applied Statistics)     Hybrid Journal   (Followers: 33)
Journal of the Royal Statistical Society, Series A (Statistics in Society)     Hybrid Journal   (Followers: 27)
Journal of the Royal Statistical Society, Series B (Statistical Methodology)     Hybrid Journal   (Followers: 43)
Journal of Theoretical Probability     Hybrid Journal   (Followers: 3)
Journal of Time Series Analysis     Hybrid Journal   (Followers: 16)
Journal of Urbanism: International Research on Placemaking and Urban Sustainability     Hybrid Journal   (Followers: 30)
Law, Probability and Risk     Hybrid Journal   (Followers: 8)
Lifetime Data Analysis     Hybrid Journal   (Followers: 7)
Mathematical Methods of Statistics     Hybrid Journal   (Followers: 4)
Measurement Interdisciplinary Research and Perspectives     Hybrid Journal   (Followers: 1)
Metrika     Hybrid Journal   (Followers: 4)
Modelling of Mechanical Systems     Full-text available via subscription   (Followers: 1)
Monte Carlo Methods and Applications     Hybrid Journal   (Followers: 6)
Monthly Statistics of International Trade - Statistiques mensuelles du commerce international     Full-text available via subscription   (Followers: 2)
Multivariate Behavioral Research     Hybrid Journal   (Followers: 5)
Optimization Letters     Hybrid Journal   (Followers: 2)
Optimization Methods and Software     Hybrid Journal   (Followers: 8)
Oxford Bulletin of Economics and Statistics     Hybrid Journal   (Followers: 34)
Pharmaceutical Statistics     Hybrid Journal   (Followers: 17)
Probability Surveys     Open Access   (Followers: 4)
Queueing Systems     Hybrid Journal   (Followers: 7)
Research Synthesis Methods     Hybrid Journal   (Followers: 8)
Review of Economics and Statistics     Hybrid Journal   (Followers: 128)
Review of Socionetwork Strategies     Hybrid Journal  
Risk Management     Hybrid Journal   (Followers: 15)
Sankhya A     Hybrid Journal   (Followers: 2)
Scandinavian Journal of Statistics     Hybrid Journal   (Followers: 9)
Sequential Analysis: Design Methods and Applications     Hybrid Journal  
Significance     Hybrid Journal   (Followers: 7)
Sociological Methods & Research     Hybrid Journal   (Followers: 38)
SourceOCDE Comptes nationaux et Statistiques retrospectives     Full-text available via subscription  
SourceOCDE Statistiques : Sources et methodes     Full-text available via subscription  
SourceOECD Bank Profitability Statistics - SourceOCDE Rentabilite des banques     Full-text available via subscription   (Followers: 1)
SourceOECD Insurance Statistics - SourceOCDE Statistiques d'assurance     Full-text available via subscription   (Followers: 2)
SourceOECD Main Economic Indicators - SourceOCDE Principaux indicateurs economiques     Full-text available via subscription   (Followers: 1)
SourceOECD Measuring Globalisation Statistics - SourceOCDE Mesurer la mondialisation - Base de donnees statistiques     Full-text available via subscription  
SourceOECD Monthly Statistics of International Trade     Full-text available via subscription   (Followers: 1)
SourceOECD National Accounts & Historical Statistics     Full-text available via subscription  
SourceOECD OECD Economic Outlook Database - SourceOCDE Statistiques des Perspectives economiques de l'OCDE     Full-text available via subscription   (Followers: 2)
SourceOECD Science and Technology Statistics - SourceOCDE Base de donnees des sciences et de la technologie     Full-text available via subscription  
SourceOECD Statistics Sources & Methods     Full-text available via subscription   (Followers: 1)
SourceOECD Taxing Wages Statistics - SourceOCDE Statistiques des impots sur les salaires     Full-text available via subscription  
Stata Journal     Full-text available via subscription   (Followers: 9)
Statistica Neerlandica     Hybrid Journal   (Followers: 1)
Statistical Applications in Genetics and Molecular Biology     Hybrid Journal   (Followers: 5)
Statistical Communications in Infectious Diseases     Hybrid Journal  
Statistical Inference for Stochastic Processes     Hybrid Journal   (Followers: 3)
Statistical Methodology     Hybrid Journal   (Followers: 7)
Statistical Methods and Applications     Hybrid Journal   (Followers: 6)
Statistical Methods in Medical Research     Hybrid Journal   (Followers: 27)
Statistical Modelling     Hybrid Journal   (Followers: 19)
Statistical Papers     Hybrid Journal   (Followers: 4)
Statistical Science     Full-text available via subscription   (Followers: 13)
Statistics & Probability Letters     Hybrid Journal   (Followers: 13)
Statistics & Risk Modeling     Hybrid Journal   (Followers: 3)
Statistics and Computing     Hybrid Journal   (Followers: 13)
Statistics and Economics     Open Access   (Followers: 1)
Statistics in Medicine     Hybrid Journal   (Followers: 195)
Statistics, Politics and Policy     Hybrid Journal   (Followers: 6)
Statistics: A Journal of Theoretical and Applied Statistics     Hybrid Journal   (Followers: 14)
Stochastic Models     Hybrid Journal   (Followers: 3)
Stochastics An International Journal of Probability and Stochastic Processes: formerly Stochastics and Stochastics Reports     Hybrid Journal   (Followers: 2)
Structural and Multidisciplinary Optimization     Hybrid Journal   (Followers: 12)
Teaching Statistics     Hybrid Journal   (Followers: 7)
Technology Innovations in Statistics Education (TISE)     Open Access   (Followers: 2)
TEST     Hybrid Journal   (Followers: 3)
The American Statistician     Full-text available via subscription   (Followers: 23)
The Annals of Applied Probability     Full-text available via subscription   (Followers: 8)
The Annals of Probability     Full-text available via subscription   (Followers: 10)
The Annals of Statistics     Full-text available via subscription   (Followers: 34)
The Canadian Journal of Statistics / La Revue Canadienne de Statistique     Hybrid Journal   (Followers: 11)
Wiley Interdisciplinary Reviews - Computational Statistics     Hybrid Journal   (Followers: 1)

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Applied Categorical Structures
Journal Prestige (SJR): 0.49
Number of Followers: 4  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1572-9095 - ISSN (Online) 0927-2852
Published by Springer-Verlag Homepage  [2655 journals]
  • The Homotopy Category of Cotorsion Flat Modules
    • Abstract: This paper aims at studying the homotopy category of cotorsion flat left modules \({{\mathbb {K}}({\mathrm{CotF}}\text {-}R)}\) over a ring R. We prove that if R is right coherent, then the homotopy category \({\mathbb {K}}(\mathrm{dg}\text {-}\mathrm{CotF}\text {-}R)\) of dg-cotorsion complexes of flat R-modules is compactly generated. This uses firstly the existence of cotorsion flat preenvelopes over such rings and, secondly, the existence of a complete cotorsion pair \(({{\mathbb {K}}_{\mathrm{p}}({\mathrm{Flat}}\text {-}R)}, {\mathbb {K}}(\mathrm{dg}\text {-}\mathrm{CotF}\text {-}R))\) in the homotopy category \({{\mathbb {K}}({\mathrm{Flat}}\text {-}R)}\) of complexes of flat R-modules, for arbitrary R. In the setting of quasi coherent sheaves over a Noetherian scheme, this cotorsion pair was discovered in the literature. However, we use a more elementary argument that gives this cotorsion pair for arbitrary R. Next we deal with cotorsion flat resolutions of complexes and define and study the notion of cotorsion flat dimension for complexes of flat R-modules. We also obtain an equivalence \({\mathbb {K}}(\mathrm{dg}\text {-}\mathrm{CotF}\text {-}R)\approx {{\mathbb {K}}({\mathrm{Proj}}\text {-}R)}\) of triangulated categories where \({{\mathbb {K}}({\mathrm{Proj}}\text {-}R)}\) is the homotopy category of projective R-modules. Combined with the aforementioned result, this recovers a result from Neeman, asserting the compact generation of \({{\mathbb {K}}({\mathrm{Proj}}\text {-}R)}\) over right coherent R. Also we get the unbounded derived category \({\mathbb {D}} (R)\) of R as a Verdier quotient of \({\mathbb {K}}(\mathrm{dg}\text {-}\mathrm{CotF}\text {-}R)\) .
      PubDate: 2021-04-01
  • Morphisms of Rational Motivic Homotopy Types
    • Abstract: We investigate several interrelated foundational questions pertaining to the study of motivic dga’s of Dan-Cohen and Schlank (Rational motivic path spaces and Kim’s relative unipotent section conjecture. arXiv:1703.10776) and Iwanari (Motivic rational homotopy type. arXiv:1707.04070). In particular, we note that morphisms of motivic dga’s can reasonably be thought of as a nonabelian analog of motivic cohomology. Just as abelian motivic cohomology is a homotopy group of a spectrum coming from K-theory, the space of morphisms of motivic dga’s is a certain limit of such spectra; we give an explicit formula for this limit—a possible first step towards explicit computations or dimension bounds. We also consider commutative comonoids in Chow motives, which we call “motivic Chow coalgebras”. We discuss the relationship between motivic Chow coalgebras and motivic dga’s of smooth proper schemes. As a small first application of our results, we show that among schemes which are finite étale over a number field, morphisms of associated motivic dga’s are no different than morphisms of schemes. This may be regarded as a small consequence of a plausible generalization of Kim’s relative unipotent section conjecture, hence as an ounce of evidence for the latter.
      PubDate: 2021-04-01
  • On Equalizers in the Category of Locales
    • Abstract: The fact that equalizers in the context of strongly Hausdorff locales (similarly like those in classical spaces) are closed is a special case of a standard categorical fact connecting diagonals with general equalizers. In this paper we analyze this and related phenomena in the category of locales. Here the mechanism of pullbacks connecting equalizers is based on natural preimages that preserve a number of properties (closedness, openness, fittedness, complementedness, etc.). Also, we have a new simple and transparent formula for equalizers in this category providing very easy proofs for some facts (including the general behavior of diagonals). In particular we discuss some aspects of the closed case (strong Hausdorff property), and the open and clopen one.
      PubDate: 2021-04-01
  • Codenseness and Openness with Respect to an Interior Operator
    • Abstract: Working in an arbitrary category endowed with a fixed \(({\mathcal {E}}, {\mathcal {M}})\) -factorization system such that \({\mathcal {M}}\) is a fixed class of monomorphisms, we first define and study a concept of codense morphisms with respect to a given categorical interior operator i. Some basic properties of these morphisms are discussed. In particular, it is shown that i-codenseness is preserved under both images and dual images under morphisms in \({\mathcal {M}}\) and \({\mathcal {E}}\) , respectively. We then introduce and investigate a notion of quasi-open morphisms with respect to i. Notably, we obtain a characterization of quasi i-open morphisms in terms of i-codense subobjects. Furthermore, we prove that these morphisms are a generalization of the i-open morphisms that are introduced by Castellini. We show that every morphism which is both i-codense and quasi i-open is actually i-open. Examples in topology and algebra are also provided.
      PubDate: 2021-04-01
  • The Chromatic Brauer Category and Its Linear Representations
    • Abstract: The Brauer category is a symmetric strict monoidal category that arises as a (horizontal) categorification of the Brauer algebras in the context of Banagl’s framework of positive topological field theories (TFTs). We introduce the chromatic Brauer category as an enrichment of the Brauer category in which the morphisms are component-wise labeled. Linear representations of the (chromatic) Brauer category are symmetric strict monoidal functors into the category of real vector spaces and linear maps equipped with the Schauenburg tensor product. We study representation theory of the (chromatic) Brauer category, and classify all its faithful linear representations. As an application, we use indices of fold lines to construct a refinement of Banagl’s concrete positive TFT based on fold maps into the plane.
      PubDate: 2021-04-01
  • Discrete and Conservative Factorizations in Fib ( B )
    • Abstract: We focus on the transfer of some known orthogonal factorization systems from \(\mathsf {Cat}\) to the 2-category \({\mathsf {Fib}}(B)\) of fibrations over a fixed base category B: the internal version of the comprehensive factorization, and the factorization systems given by (sequence of coidentifiers, discrete morphism) and (sequence of coinverters, conservative morphism) respectively. For the class of fibrewise opfibrations in \({\mathsf {Fib}}(B)\) , the construction of the latter two simplify to a single coidentifier (respectively coinverter) followed by an internal discrete opfibration (resp. fibrewise opfibration in groupoids). We show how these results follow from their analogues in \(\mathsf {Cat}\) , providing suitable conditions on a 2-category \({\mathcal {C}}\) , that allow the transfer of the construction of coinverters and coidentifiers from \({\mathcal {C}}\)  to \({\mathsf {Fib}}_{{\mathcal {C}}}(B)\) .
      PubDate: 2021-04-01
  • Subprojectivity in Abelian Categories
    • Abstract: In the last few years, López-Permouth and several collaborators have introduced a new approach in the study of the classical projectivity, injectivity and flatness of modules. This way, they introduced subprojectivity domains of modules as a tool to measure, somehow, the projectivity level of such a module (so not just to determine whether or not the module is projective). In this paper we develop a new treatment of the subprojectivity in any abelian category which shed more light on some of its various important aspects. Namely, in terms of subprojectivity, some classical results are unified and some classical rings are characterized. It is also shown that, in some categories, the subprojectivity measures notions other than the projectivity. Furthermore, this new approach allows, in addition to establishing nice generalizations of known results, to construct various new examples such as the subprojectivity domain of the class of Gorenstein projective objects, the class of semi-projective complexes and particular types of representations of a finite linear quiver. The paper ends with a study showing that the fact that a subprojectivity domain of a class coincides with its first right Ext-orthogonal class can be characterized in terms of the existence of preenvelopes and precovers.
      PubDate: 2021-03-11
  • Free bounded archimedean $$\ell $$ ℓ -algebras
    • Abstract: We show that free objects on sets do not exist in the category \({\varvec{ba}}\varvec{\ell }\) of bounded archimedean \(\ell \) -algebras. On the other hand, we introduce the category of weighted sets and prove that free objects on weighted sets do exist in \({\varvec{ba}}\varvec{\ell }\) . We conclude by discussing several consequences of this result.
      PubDate: 2021-03-09
  • (Lack of) Model Structures on the Category of Graphs
    • Abstract: In this article, we study model structures on the category of finite graphs with \(\times \) -homotopy equivalences as the weak equivalences. We show that there does not exist an analogue of Strøm-Hurewicz model structure on this category of graphs. More interestingly, we show that this category of graphs with \(\times \) -homotopy equivalences does not have a model structure whenever the class of cofibrations is a subclass of graph inclusions.
      PubDate: 2021-03-04
  • Mapping Ideals to Sublocales
    • Abstract: A map that is well known in C(X), dating back to the work of L. Gillman, M. Henriksen and M. Jerison in 1954, is here used to construct a morphism of quantales, whose right adjoint we show to be the map that sends a subset A of \(\beta X\) to the ideal $$\begin{aligned} {\varvec{O}}^A =\{f\in C(X)\mid A\subseteq {{\,\mathrm{int}\,}}_{\beta X}{{\,\mathrm{cl}\,}}_{\beta X}Z(f)\} \end{aligned}$$ of C(X) if and only if X is a P-space. We show that when viewed this way, this map characterizes R.G. Woods’ WN-maps in terms of commutativity of a certain diagram in the category of quantales. All this is achieved most economically by working with locales instead of topological spaces. The Lindelöf reflection allows us to present “countable” analogues of the results just mentioned and we highlight the similarities and disparities.
      PubDate: 2021-03-03
  • Totally Acyclic Approximations
    • Abstract: Let \(Q \rightarrow R\) be a surjective homomorphism of Noetherian rings such that Q is Gorenstein and R as a Q-bimodule admits a finite resolution by modules which are projective on both sides. We define an adjoint pair of functors between the homotopy category of totally acyclic R-complexes and that of Q-complexes. This adjoint pair is analogous to the classical adjoint pair of functors between the module categories of R and Q. As a consequence, we obtain a precise notion of approximations of totally acyclic R-complexes by totally acyclic Q-complexes.
      PubDate: 2021-02-20
  • Tannaka Duality, Coclosed Categories and Reconstruction for Nonarchimedean
    • Abstract: The topic of this paper is a generalization of Tannaka duality to coclosed categories. As an application we prove reconstruction theorems for coalgebras (bialgebras, Hopf algebras) in categories of topological vector spaces over a nonarchimedean field K. In particular, our results imply reconstruction and recognition theorems for categories of locally analytic representations of compact p-adic groups, which was the major motivation for this work.
      PubDate: 2021-02-20
  • An Essential, Hyperconnected, Local Geometric Morphism that is not Locally
    • Abstract: Thomas Streicher asked on the category theory mailing list whether every essential, hyperconnected, local geometric morphism is automatically locally connected. We show that this is not the case, by providing a counterexample.
      PubDate: 2021-02-15
  • Tropical Duality in $$(d+2)$$ ( d + 2 ) -Angulated Categories
    • Abstract: Let \(\mathscr {C}\) be a 2-Calabi–Yau triangulated category with two cluster tilting subcategories \(\mathscr {T}\) and \(\mathscr {U}\) . A result from Jørgensen and Yakimov (Sel Math (NS) 26:71–90, 2020) and Demonet et al. (Int Math Res Not 2019:852–892, 2017) known as tropical duality says that the index with respect to \(\mathscr {T}\) provides an isomorphism between the split Grothendieck groups of \(\mathscr {U}\) and \(\mathscr {T}\) . We also have the notion of c-vectors, which using tropical duality have been proven to have sign coherence, and to be recoverable as dimension vectors of modules in a module category. The notion of triangulated categories extends to the notion of \((d+2)\) -angulated categories. Using a higher analogue of cluster tilting objects, this paper generalises tropical duality to higher dimensions. This implies that these basic cluster tilting objects have the same number of indecomposable summands. It also proves that under conditions of mutability, c-vectors in the \((d+2)\) -angulated case have sign coherence, and shows formulae for their computation. Finally, it proves that under the condition of mutability, the c-vectors are recoverable as dimension vectors of modules in a module category.
      PubDate: 2021-02-06
      DOI: 10.1007/s10485-020-09625-7
  • Maurer–Cartan Moduli and Theorems of Riemann–Hilbert Type
    • Abstract: We study Maurer–Cartan moduli spaces of dg algebras and associated dg categories and show that, while not quasi-isomorphism invariants, they are invariants of strong homotopy type, a natural notion that has not been studied before. We prove, in several different contexts, Schlessinger–Stasheff type theorems comparing the notions of homotopy and gauge equivalence for Maurer–Cartan elements as well as their categorified versions. As an application, we re-prove and generalize Block–Smith’s higher Riemann–Hilbert correspondence, and develop its analogue for simplicial complexes and topological spaces.
      PubDate: 2021-02-06
      DOI: 10.1007/s10485-021-09631-3
  • Functoriality of Groupoid Quantale. II
    • Abstract: Taking advantage of the quantale-theoretic description of étale groupoids we study principal bundles, Hilsum–Skandalis maps, and Morita equivalence by means of modules on inverse quantal frames. The Hilbert module description of quantale sheaves leads naturally to a formulation of Morita equivalence in terms of bimodules that resemble imprimitivity bimodules of C*-algebras.
      PubDate: 2021-02-01
      DOI: 10.1007/s10485-021-09628-y
  • The Kechris–Pestov–Todorčević Correspondence from the Point of View
           of Category Theory
    • Abstract: The Kechris–Pestov–Todorčević correspondence (KPT-correspondence for short) is a surprising correspondence between model theory, combinatorics and topological dynamics. In this paper we present a categorical re-interpretation of (a part of) the KPT-correspondence with the aim of proving a dual statement. Our strategy is to take a “direct” result and then analyze the necessary infrastructure that makes the result true by providing a purely categorical proof of the categorical version of the result. We can then capitalize on the Duality Principle to obtain the dual statements almost for free. We believe that the dual version of the KPT-correspondence can not only provide the new insights into the interplay of combinatorial, model-theoretic and topological phenomena this correspondence binds together, but also explores the limits to which categorical treatment of combinatorial phenomena can take us.
      PubDate: 2021-02-01
      DOI: 10.1007/s10485-020-09611-z
  • Vector Bundles and Differential Bundles in the Category of Smooth
    • Abstract: A tangent category is a category equipped with an endofunctor that satisfies certain axioms which capture the abstract properties of the tangent bundle functor from classical differential geometry. Cockett and Cruttwell introduced differential bundles in 2017 as an algebraic alternative to vector bundles in an arbitrary tangent category. In this paper, we prove that differential bundles in the category of smooth manifolds are precisely vector bundles. In particular, this means that we can give a characterisation of vector bundles that exhibits them as models of a tangent categorical essentially algebraic theory.
      PubDate: 2021-01-02
      DOI: 10.1007/s10485-020-09617-7
  • A Constructive Approach to Freyd Categories
    • Abstract: We discuss Peter Freyd’s universal way of equipping an additive category \(\mathbf {P}\) with cokernels from a constructive point of view. The so-called Freyd category \(\mathcal {A}(\mathbf {P})\) is abelian if and only if \(\mathbf {P}\) has weak kernels. Moreover, \(\mathcal {A}(\mathbf {P})\) has decidable equality for morphisms if and only if we have an algorithm for solving linear systems \(X \cdot \alpha = \beta \) for morphisms \(\alpha \) and \(\beta \) in \(\mathbf {P}\) . We give an example of an additive category with weak kernels and decidable equality for morphisms in which the question whether such a linear system admits a solution is computationally undecidable. Furthermore, we discuss an additional computational structure for \(\mathbf {P}\) that helps solving linear systems in \(\mathbf {P}\) and even in the iterated Freyd category construction \(\mathcal {A}( \mathcal {A}(\mathbf {P})^{\mathrm {op}} )\) , which can be identified with the category of finitely presented covariant functors on \(\mathcal {A}(\mathbf {P})\) . The upshot of this paper is a constructive approach to finitely presented functors that subsumes and enhances the standard approach to finitely presented modules in computer algebra.
      PubDate: 2020-10-13
      DOI: 10.1007/s10485-020-09612-y
  • Gabriel–Zisman Cohomology and Spectral Sequences
    • Abstract: Extending constructions by Gabriel and Zisman, we develop a functorial framework for the cohomology and homology of simplicial sets with very general coefficient systems given by functors on simplex categories into abelian categories. Furthermore we construct Leray type spectral sequences for any map of simplicial sets. We also show that these constructions generalise and unify the various existing versions of cohomology and homology of small categories and as a bonus provide new insight into their functoriality.
      PubDate: 2020-10-10
      DOI: 10.1007/s10485-020-09609-7
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