Displaying similar documents to “Homological category weights and estimates for cat 1 ( X , ξ )

On the structure of halfdiagonal-halfterminal-symmetric categories with diagonal inversions

Hans-Jürgen Vogel (2001)

Discussiones Mathematicae - General Algebra and Applications

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The category of all binary relations between arbitrary sets turns out to be a certain symmetric monoidal category Rel with an additional structure characterized by a family d = ( d A : A A A | A | R e l | ) of diagonal morphisms, a family t = ( t A : A I | A | R e l | ) of terminal morphisms, and a family = ( A : A A A | A | R e l | ) of diagonal inversions having certain properties. Using this properties in [11] was given a system of axioms which characterizes the abstract concept of a halfdiagonal-halfterminal-symmetric monoidal category with diagonal inversions (hdht∇s-category)....

Schur-Finite Motives and Trace Identities

Alessio Del Padrone, Carlo Mazza (2009)

Bollettino dell'Unione Matematica Italiana

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We provide a sufficient condition that ensures the nilpotency of endomorphisms universally of trace zero of Schur-finite objects in a category of homological type, i.e., a -linear -category with a tensor functor to super vector spaces. We present some applications in the category of motives, where our result generalizes previous results about finite-dimensional objects, in particular by Kimura. We also present some facts which suggest that this might be the best generalization possible...

Determinantal Barlow surfaces and phantom categories

Christian Böhning, Hans-Christian Graf von Bothmer, Ludmil Katzarkov, Pawel Sosna (2015)

Journal of the European Mathematical Society

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We prove that the bounded derived category of the surface S constructed by Barlow admits a length 11 exceptional sequence consisting of (explicit) line bundles. Moreover, we show that in a small neighbourhood of S in the moduli space of determinantal Barlow surfaces, the generic surface has a semiorthogonal decomposition of its derived category into a length 11 exceptional sequence of line bundles and a category with trivial Grothendieck group and Hochschild homology, called a phantom...

n -angulated quotient categories induced by mutation pairs

Zengqiang Lin (2015)

Czechoslovak Mathematical Journal

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Geiss, Keller and Oppermann (2013) introduced the notion of n -angulated category, which is a “higher dimensional” analogue of triangulated category, and showed that certain ( n - 2 ) -cluster tilting subcategories of triangulated categories give rise to n -angulated categories. We define mutation pairs in n -angulated categories and prove that given such a mutation pair, the corresponding quotient category carries a natural n -angulated structure. This result generalizes a theorem of Iyama-Yoshino...

A note on model structures on arbitrary Frobenius categories

Zhi-wei Li (2017)

Czechoslovak Mathematical Journal

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We show that there is a model structure in the sense of Quillen on an arbitrary Frobenius category such that the homotopy category of this model structure is equivalent to the stable category ̲ as triangulated categories. This seems to be well-accepted by experts but we were unable to find a complete proof for it in the literature. When is a weakly idempotent complete (i.e., every split monomorphism is an inflation) Frobenius category, the model structure we constructed is an exact...

The categories of presheaves containing any category of algebras

V. Trnková, J. Reiterman

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ContentsIntroduction.................................................................................................................................................. 5I. Preliminaries........................................................................................................................................... 6II. Main theorem.......................................................................................................................................... 8III. The...

Base change for Picard-Vessiot closures

Andy R. Magid (2011)

Banach Center Publications

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The differential automorphism group, over F, Π₁(F₁) of the Picard-Vessiot closure F₁ of a differential field F is a proalgebraic group over the field C F of constants of F, which is assumed to be algebraically closed of characteristic zero, and its category of C F modules is equivalent to the category of differential modules over F. We show how this group and the category equivalence behave under a differential extension E ⊃ F, where C E is also algebraically closed.

Various categorical approaches to statistical spaces

Tadeusz Bromek, Maria Moszyńska

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CONTENTSIntroduction..............................................................................................................51. Preliminaries........................................................................................................61.0. Measurable, probabilistic, and statistical spaces..............................................61.1. Transition functions..........................................................................................61.2. Linear space of...

A general theory of polyhedral sets and the corresponding T-complexes

David W. Jones

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PrefaceThis paper is essentially David Jones' 1984 University of Wales Ph. D. Thesis, "Poly-T-complexes". It is published concurrently with Asley, 1988.The main aim is to find a setting for the most general kinds of geometrically defined compositions. Thus it comes under the slogan: "Find an algebraic inverse to subdivision". In the background is the Generalised Van Kampen Theorem, whose proof uses in an essential way general compositions of cubes. An even older background is the idea...

Yetter-Drinfeld-Long bimodules are modules

Daowei Lu, Shuan Hong Wang (2017)

Czechoslovak Mathematical Journal

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Let H be a finite-dimensional bialgebra. In this paper, we prove that the category ℒℛ ( H ) of Yetter-Drinfeld-Long bimodules, introduced by F. Panaite, F. Van Oystaeyen (2008), is isomorphic to the Yetter-Drinfeld category H H * H H * 𝒴𝒟 over the tensor product bialgebra H H * as monoidal categories. Moreover if H is a finite-dimensional Hopf algebra with bijective antipode, the isomorphism is braided. Finally, as an application of this category isomorphism, we give two results.

The Brauer category and invariant theory

Gustav I. Lehrer, R. B. Zhang (2015)

Journal of the European Mathematical Society

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A category of Brauer diagrams, analogous to Turaev’s tangle category, is introduced, a presentation of the category is given, and full tensor functors are constructed from this category to the category of tensor representations of the orthogonal group O ( V ) or the symplectic group Sp ( V ) over any field of characteristic zero. The first and second fundamental theorems of invariant theory for these classical groups are generalised to the category theoretic setting. The major outcome is that...

The logic of categories of partial functions and its applications

Adam Obtułowicz

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CONTENTS0. Introduction.......................................................................................................................................................................................51. Preliminaries.....................................................................................................................................................................................92. Relations and functional relations in a category.............................................................................................................................13 2.1....

Two results of n -exangulated categories

Jian He, Jing He, Panyue Zhou (2024)

Czechoslovak Mathematical Journal

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M. Herschend, Y. Liu, H. Nakaoka introduced n -exangulated categories, which are a simultaneous generalization of n -exact categories and ( n + 2 ) -angulated categories. This paper consists of two results on n -exangulated categories: (1) we give an equivalent characterization of axiom (EA2); (2) we provide a new way to construct a closed subfunctor of an n -exangulated category.

On Lusternik-Schnirelmann category of SO(10)

Norio Iwase, Toshiyuki Miyauchi (2016)

Fundamenta Mathematicae

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Let G be a compact connected Lie group and p: E → ΣA be a principal G-bundle with a characteristic map α: A → G, where A = ΣA₀ for some A₀. Let K i F i - 1 F i | 1 i m with F₀ = ∗, F₁ = ΣK₁ and Fₘ ≃ G be a cone-decomposition of G of length m and F’₁ = ΣK’₁ ⊂ F₁ with K’₁ ⊂ K₁ which satisfy F i F ' F i + 1 up to homotopy for all i. Then cat(E) ≤ m + 1, under suitable conditions, which is used to determine cat(SO(10)). A similar result was obtained by Kono and the first author (2007) to determine cat(Spin(9)), but that result...

On uniquely partitionable relational structures and object systems

Jozef Bucko, Peter Mihók (2006)

Discussiones Mathematicae Graph Theory

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We introduce object systems as a common generalization of graphs, hypergraphs, digraphs and relational structures. Let C be a concrete category, a simple object system over C is an ordered pair S = (V,E), where E = A₁,A₂,...,Aₘ is a finite set of the objects of C, such that the ground-set V ( A i ) of each object A i E is a finite set with at least two elements and V i = 1 m V ( A i ) . To generalize the results on graph colourings to simple object systems we define, analogously as for graphs, that an additive induced-hereditary...

On the structure of triangulated categories with finitely many indecomposables

Claire Amiot (2007)

Bulletin de la Société Mathématique de France

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We study the problem of classifying triangulated categories with finite-dimensional morphism spaces and finitely many indecomposables over an algebraically closed field k . We obtain a new proof of the following result due to Xiao and Zhu: the Auslander-Reiten quiver of such a category 𝒯 is of the form Δ / G where Δ is a disjoint union of simply-laced Dynkin diagrams and G a weakly admissible group of automorphisms of Δ . Then we prove that for ‘most’ groups G , the category 𝒯 is standard, ...

Strong Fubini properties for measure and category

Krzysztof Ciesielski, Miklós Laczkovich (2003)

Fundamenta Mathematicae

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Let (FP) abbreviate the statement that 0 1 ( 0 1 f d y ) d x = 0 1 ( 0 1 f d x ) d y holds for every bounded function f: [0,1]² → ℝ whenever each of the integrals involved exists. We shall denote by (SFP) the statement that the equality above holds for every bounded function f: [0,1]² → ℝ having measurable vertical and horizontal sections. It follows from well-known results that both of (FP) and (SFP) are independent of the axioms of ZFC. We investigate the logical connections of these statements with several other strong Fubini...

Derived endo-discrete artin algebras

Raymundo Bautista (2006)

Colloquium Mathematicae

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Let Λ be an artin algebra. We prove that for each sequence ( h i ) i of non-negative integers there are only a finite number of isomorphism classes of indecomposables X b ( Λ ) , the bounded derived category of Λ, with l e n g t h E ( X ) H i ( X ) = h i for all i ∈ ℤ and E(X) the endomorphism ring of X in b ( Λ ) if and only if b ( M o d Λ ) , the bounded derived category of the category M o d Λ of all left Λ-modules, has no generic objects in the sense of [4].

Generic representations of orthogonal groups: projective functors in the category q u a d

Christine Vespa (2008)

Fundamenta Mathematicae

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We continue the study of the category of functors q u a d , associated to ₂-vector spaces equipped with a nondegenerate quadratic form, initiated in J. Pure Appl. Algebra 212 (2008) and Algebr. Geom. Topology 7 (2007). We define a filtration of the standard projective objects in q u a d ; this refines to give a decomposition into indecomposable factors of the first two standard projective objects in q u a d : P H and P H . As an application of these two decompositions, we give a complete description of the polynomial...

How to construct a Hovey triple from two cotorsion pairs

James Gillespie (2015)

Fundamenta Mathematicae

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Let be an abelian category, or more generally a weakly idempotent complete exact category, and suppose we have two complete hereditary cotorsion pairs ( , ˜ ) and ( ˜ , ) in satisfying ˜ and ˜ = ˜ . We show how to construct a (necessarily unique) abelian model structure on with (resp. ˜ ) as the class of cofibrant (resp. trivially cofibrant) objects, and (resp. ˜ ) as the class of fibrant (resp. trivially fibrant) objects.

On category 𝒪 for cyclotomic rational Cherednik algebras

Iain G. Gordon, Ivan Losev (2014)

Journal of the European Mathematical Society

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We study equivalences for category 𝒪 p of the rational Cherednik algebras 𝐇 p of type G ( n ) = ( μ ) n 𝔖 n : a highest weight equivalence between 𝒪 p and 𝒪 σ ( p ) for σ 𝔖 and an action of 𝔖 on an explicit non-empty Zariski open set of parameters p ; a derived equivalence between 𝒪 p and 𝒪 p ' whenever p and p ' have integral difference; a highest weight equivalence between 𝒪 p and a parabolic category 𝒪 for the general linear group, under a non-rationality assumption on the parameter p . As a consequence, we confirm special cases...

On stable equivalences of module subcategories over a semiperfect noetherian ring

Noritsugu Kameyama, Yuko Kimura, Kenji Nishida (2014)

Colloquium Mathematicae

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Given a semiperfect two-sided noetherian ring Λ, we study two subcategories k ( Λ ) = M m o d Λ | E x t Λ j ( T r M , Λ ) = 0 ( 1 j k ) and k ( Λ ) = N m o d Λ | E x t Λ j ( N , Λ ) = 0 ( 1 j k ) of the category mod Λ of finitely generated right Λ-modules, where Tr M is Auslander’s transpose of M. In particular, we give another convenient description of the categories k ( Λ ) and k ( Λ ) , and we study category equivalences and stable equivalences between them. Several results proved in [J. Algebra 301 (2006), 748-780] are extended to the case when Λ is a two-sided noetherian semiperfect ring.