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Relevant bibliographies by topics / Categories (Algebra)

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Academic literature on the topic 'Categories (Algebra)'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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Journal articles on the topic "Categories (Algebra)"

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AQUINO, R. M., E. N. MARCOS, and S. TREPODE. "ON THE EXISTENCE OF A DERIVED EQUIVALENCE BETWEEN A KOSZUL ALGEBRA AND ITS YONEDA ALGEBRA." Journal of Algebra and Its Applications 13, no. 04 (2014): 1350136. http://dx.doi.org/10.1142/s0219498813501363.

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In this paper, we study the derived categories of a Koszul algebra and its Yoneda algebra to determine when those categories are triangularly equivalent. We prove that the simply connected Koszul algebras are derived equivalent to their Yoneda algebras. We have considered discrete Koszul algebras and we gave necessary and sufficient conditions for those Koszul algebras to be derived equivalent to their Yoneda algebras. We also study the class of Koszul algebras which are derived equivalent to hereditary algebras. For the case where the hereditary algebra is tame, we characterized the derived e

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Васюков, Владимир Леонидович. "Quantum categories for quantum logic." Logical Investigations 25, no. 1 (2019): 70–87. http://dx.doi.org/10.21146/2074-1472-2019-25-1-70-87.

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The paper is the contribution to quantum toposophy focusing on the abstract orthomodular structures (following Dunn-Moss-Wang terminology). Early quantum toposophical approach to "abstract quantum logic" was proposed based on the topos of functors $\mathsf{[E,Sets]}$ where $\mathsf{E}$ is a so-called orthomodular preorder category – a modification of categorically rewritten orthomodular lattice (taking into account that like any lattice it will be a finite co-complete preorder category). In the paper another kind of categorical semantics of quantum logic is discussed which is based on the modi

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Wiedemann, Alfred. "On Stratifications of Derived Module Categories." Canadian Mathematical Bulletin 34, no. 2 (1991): 275–80. http://dx.doi.org/10.4153/cmb-1991-044-0.

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AbstractSome structural results about quotients and tensor products of hereditary respectively quasi-hereditary algebras are presented. They are related to properties of stratifications of derived module categories. The concept of derived-simplicity for an algebra is introduced and studied.

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SANTIAGO, VALENTE. "STRATIFYING SYSTEMS FOR EXACT CATEGORIES." Glasgow Mathematical Journal 61, no. 03 (2018): 501–21. http://dx.doi.org/10.1017/s0017089518000320.

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AbstractIn this paper, we develop the theory of stratifying systems in the context of exact categories as a generalisation of the notion of stratifying systems in module categories, which have been studied by different authors. We prove that attached to a stratifying system in an exact category $(\mathcal{A},\mathcal{E})$ there is an standardly stratified algebra B such that the category $\mathscr{F}$F(Θ), of F-filtered objects in the exact category $(\mathcal{A},\mathcal{E})$ is equivalent to the category $\mathscr{F}$(Δ) of Δ-good modules associated to B. The theory we develop in exact categ

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BAUR, KARIN, DUSKO BOGDANIC, and ANA GARCIA ELSENER. "CLUSTER CATEGORIES FROM GRASSMANNIANS AND ROOT COMBINATORICS." Nagoya Mathematical Journal 240 (June 3, 2019): 322–54. http://dx.doi.org/10.1017/nmj.2019.14.

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The category of Cohen–Macaulay modules of an algebra $B_{k,n}$ is used in Jensen et al. (A categorification of Grassmannian cluster algebras, Proc. Lond. Math. Soc. (3) 113(2) (2016), 185–212) to give an additive categorification of the cluster algebra structure on the homogeneous coordinate ring of the Grassmannian of $k$-planes in $n$-space. In this paper, we find canonical Auslander–Reiten sequences and study the Auslander–Reiten translation periodicity for this category. Furthermore, we give an explicit construction of Cohen–Macaulay modules of arbitrary rank. We then use our results to es

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Neshveyev, Sergey, and Makoto Yamashita. "A Few Remarks on the Tube Algebra of a Monoidal Category." Proceedings of the Edinburgh Mathematical Society 61, no. 3 (2018): 735–58. http://dx.doi.org/10.1017/s0013091517000426.

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AbstractWe prove two results on the tube algebras of rigid C*-tensor categories. The first is that the tube algebra of the representation category of a compact quantum groupGis a full corner of the Drinfeld double ofG. As an application, we obtain some information on the structure of the tube algebras of the Temperley–Lieb categories 𝒯ℒ(d) ford> 2. The second result is that the tube algebras of weakly Morita equivalent C*-tensor categories are strongly Morita equivalent. The corresponding linking algebra is described as the tube algebra of the 2-category defining the Morita context.

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STEINBERG, BENJAMIN, and BRET TILSON. "CATEGORIES AS ALGEBRA, II." International Journal of Algebra and Computation 13, no. 06 (2003): 627–703. http://dx.doi.org/10.1142/s021819670300150x.

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A theory of the semidirect product of categories and the derived category of a category morphism is presented. In order to include division (≺) in this theory, the traditional setting of these constructions is expanded to include relational arrows. In this expanded setting, a relational morphism φ : M → N of categories determines an optimal decomposition [Formula: see text] where [Formula: see text] denotes semidirect product and D(φ) is the derived category of φ.The theory of the semidirect product of varieties of categories, V * W, is developed. Associated with each variety V of categories i

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Keller, Bernhard, and Idun Reiten. "Acyclic Calabi–Yau categories." Compositio Mathematica 144, no. 5 (2008): 1332–48. http://dx.doi.org/10.1112/s0010437x08003540.

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AbstractWe prove a structure theorem for triangulated Calabi–Yau categories: an algebraic 2-Calabi–Yau triangulated category over an algebraically closed field is a cluster category if and only if it contains a cluster-tilting subcategory whose quiver has no oriented cycles. We prove a similar characterization for higher cluster categories. As an application to commutative algebra, we show that the stable category of maximal Cohen–Macaulay modules over a certain isolated singularity of dimension 3 is a cluster category. This implies the classification of the rigid Cohen–Macaulay modules first

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Fresse, Benoit. "Props in model categories and homotopy invariance of structures." gmj 17, no. 1 (2010): 79–160. http://dx.doi.org/10.1515/gmj.2010.007.

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Abstract We prove that any category of props in a symmetric monoidal model category inherits a model structure. We devote an appendix, about half the size of the paper, to the proof of the model category axioms in a general setting. We need the general argument to address the case of props in topological spaces and dg-modules over an arbitrary ring, but we give a less technical proof which applies to the category of props in simplicial sets, simplicial modules, and dg-modules over a ring of characteristic 0. We apply the model structure of props to the homotopical study of algebras over a prop

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Barnum, Howard, Matthew A. Graydon, and Alexander Wilce. "Composites and Categories of Euclidean Jordan Algebras." Quantum 4 (November 8, 2020): 359. http://dx.doi.org/10.22331/q-2020-11-08-359.

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We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras (EJAs), satisfying some reasonable additional constraints motivated by the desire to construct dagger-compact categories of such models. We show that no such composite has the exceptional Jordan algebra as a direct summand, nor does any such composite exist if one factor has an exceptional summand, unless the other factor is a direct sum of one-dimensional Jordan algebras (representing essentially a classical system). Moreover, we show that any composite of simple, non-exceptional EJAs is a

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Dissertations / Theses on the topic "Categories (Algebra)"

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Matsson, Isak. "Algebras in Monoidal Categories." Thesis, Uppsala universitet, Algebra och geometri, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-447430.

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Ahlsén, Daniel. "Classifying Categories : The Jordan-Hölder and Krull-Schmidt-Remak Theorems for Abelian Categories." Thesis, Uppsala universitet, Algebra och geometri, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-352383.

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Raskin, Samuel David. "Chiral Principal Series Categories." Thesis, Harvard University, 2014. http://dissertations.umi.com/gsas.harvard:11525.

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This thesis begins a study of principal series categories in geometric representation theory using the Beilinson-Drinfeld theory of chiral algebras. We study Whittaker objects in the unramified principal series category. This provides an alternative approach to the Arkhipov-Bezrukavnikov theory of Iwahori-Whittaker sheaves that exploits the geometry of the Feigin-Frenkel semi-infinite flag manifold.<br>Mathematics

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Lack, Stephen Geoffrey. "The algebra of distributive and extensive categories." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.266367.

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Kelly, Jack. "Exact categories, Koszul duality, and derived analytic algebra." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:27064241-0ad3-49c3-9d7d-870d51fe110b.

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Recent work of Bambozzi, Ben-Bassat, and Kremnitzer suggests that derived analytic geometry over a valued field k can be modelled as geometry relative to the quasi-abelian category of Banach spaces, or rather its completion Ind(Ban<sub>k</sub>). In this thesis we develop a robust theory of homotopical algebra in Ch(E) for E any sufficiently 'nice' quasi-abelian, or even exact, category. Firstly we provide sufficient conditions on weakly idempotent complete exact categories E such that various categories of chain complexes in E are equipped with projective model structures. In particular we sho

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Burton, Cynthia L. "Hopf algebras and Dieudonné modules /." Thesis, Connect to this title online; UW restricted, 1998. http://hdl.handle.net/1773/5808.

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Brown, Carolyn T. "Linear logic and Petri nets : categories, algebra and proof." Thesis, University of Edinburgh, 1990. http://hdl.handle.net/1842/15424.

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This thesis explores three ways in which linear logic may be used to define a specification language for Petri nets, by giving precise correspondences, at different levels, between linear logic and Petri nets. Firstly, we define categories NC by analogy with de Paiva's dialectica categories GC. The category NSet has as objects the elementary Petri nets and morphisms refinement maps. We show that GC induces in NC sufficient structure for NC to be a sound model of linear logic. We demonstrate the computational significance of the net constructors induced by the interpretations in NSet of the lin

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Monserrat, Antich Miquel. "Machines in closed categories in general and in categories of heyting Algebra valued sets in particular." Thesis, McGill University, 1990. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=59807.

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A survey of the minimal realization theory of Arbib and Manes for "state-behavior" machines in a category is given, and how the closed category machines of Goguen are included in the above machines is discussed in detail. A survey of the non-deterministic treatment due to Arbib and Manes is given. A study of C-machines in a closed category for a monoid C is given in both the deterministic and the non-deterministic cases. A notion of u-machine in a topos for a morphism of monoids u is introduced and studied. A discussion of the category of H-valued sets as a topos is given and finally some of t

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Scherotzke, Sarah. "On Auslander-Reiten theory for algebras and derived categories." Thesis, University of Oxford, 2009. http://ora.ox.ac.uk/objects/uuid:ad4cd5a8-34b6-4725-a2a4-a3f08994618b.

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This thesis consists of three parts. In the first part we look at Hopf algebras. We classify pointed rank one Hopf algebras over fields of prime characteristic which are generated as algebras by the first term of the coradical filtration. These Hopf algebras were classified by Radford and Krop for fields of characteristic zero. We obtain three types of Hopf algebras presented by generators and relations. The third type is new and has not previously appeared in literature. The second part of this thesis deals with Auslander-Reiten theory of finitedimensional algebras over fields. We consider G-

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Ellingsen, Steinar. "Degeneration as a Partial Order on Module Categories." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2007. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9619.

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<p>Chapter 1 contains most of the background material for this thesis. In Chapter 2 we provide a formal method for determining degeneration for algebras of finite representation type. In Chapter 3 we give an alternative procedure for finding algebraic equations determining the orbit closure of a representation.</p>

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Books on the topic "Categories (Algebra)"

1

service), SpringerLink (Online, ed. Categories and Commutative Algebra. Springer-Verlag Berlin Heidelberg, 2011.

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Salmon, P., ed. Categories and Commutative Algebra. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-10979-9.

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Zelmanowitz, Julius Martin. Duality for module categories. Verlag Reinhard Fischer, 1988.

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Categories of commutative algebras. Clarendon Press, 1992.

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Borceux, Francis. Handbook of categorical algebra. Cambridge University Press, 1994.

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W, Anderson Frank. Rings and categories of modules. 2nd ed. Springer-Verlag, 1992.

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Jiří, Rosický, and Vitale E. M, eds. Algebraic theories: A categorical introduction to general algebra. Cambridge University Press, 2010.

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8

Dodson, C. T. J. Categories, Bundles and Spacetime Topology. Springer Netherlands, 1988.

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9

Tensor categories. American Mathematical Society, 2015.

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Bautista, R. Differential tensor algebras and their module categories. Cambridge University Press, 2009.

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Book chapters on the topic "Categories (Algebra)"

1

Plotkin, B. "Categories." In Universal Algebra, Algebraic Logic, and Databases. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0820-1_4.

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Osborne, M. Scott. "Categories." In Basic Homological Algebra. Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1278-2_1.

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Kostrikin, A. I., and I. R. Shafarevich. "Triangulated Categories." In Homological Algebra. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57911-0_5.

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Gorodentsev, Alexey L. "Categories and Functors." In Algebra II. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-50853-5_9.

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Cohn, P. M. "Lattices and Categories." In Basic Algebra. Springer London, 2003. http://dx.doi.org/10.1007/978-0-85729-428-9_3.

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Gelfand, Sergei I., and Yuri I. Manin. "Triangulated Categories." In Methods of Homological Algebra. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-662-03220-6_4.

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Kostrikin, A. I., and I. R. Shafarevich. "The Language of Categories." In Homological Algebra. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57911-0_2.

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Zimmermann, Alexander. "Stable Module Categories." In Algebra and Applications. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-07968-4_5.

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Kostrikin, A. I., and I. R. Shafarevich. "Derived Categories and Derived Functors." In Homological Algebra. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57911-0_4.

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Patras, Frédéric. "Universal Phenomena, Algebra, Categories." In Lecture Notes in Mathematics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56700-2_15.

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Conference papers on the topic "Categories (Algebra)"

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Gukov, Sergei, and Marko Stošić. "Homological algebra of knots and BPS states." In Low-dimensional manifolds and high-dimensional categories -- A conference in honor of Michael Hartley Freedman. Mathematical Sciences Publishers, 2013. http://dx.doi.org/10.2140/gtm.2012.18.309.

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ŠOSTAK, ALEXANDER P. "L-VALUED CATEGORIES: GENERALITIES AND EXAMPLES RELATED TO ALGEBRA AND TOPOLOGY." In Proceedings of the North-West European Category Seminar. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702418_0022.

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ALB, ALINA. "SOME COREFLECTIVE CATEGORIES OF TOPOLOGICAL MODULES." In Proceedings of the International Conference on Algebras, Modules and Rings. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774552_0001.

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Hadi, Ibnu, Yudi Mahatma, and Sudarwanto. "The categories of supermodules over different algebras." In THE 2ND SCIENCE AND MATHEMATICS INTERNATIONAL CONFERENCE (SMIC 2020): Transforming Research and Education of Science and Mathematics in the Digital Age. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0045369.

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Mucuk, Osman, and Serap Demir. "Internal categories in the category of semi abelian algebras." In FOURTH INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0042238.

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Beschke, Sebastian, and Wolfgang Menzel. "Graph Algebraic Combinatory Categorial Grammar." In Proceedings of the Seventh Joint Conference on Lexical and Computational Semantics. Association for Computational Linguistics, 2018. http://dx.doi.org/10.18653/v1/s18-2006.

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May, J. P. "The construction of E∞ring spaces from bipermutative categories." In New topological contexts for Galois theory and algebraic geometry. Mathematical Sciences Publishers, 2009. http://dx.doi.org/10.2140/gtm.2009.16.283.

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May, J. P. "The construction of E∞ring spaces from bipermutative categories." In New topological contexts for Galois theory and algebraic geometry. Mathematical Sciences Publishers, 2009. http://dx.doi.org/10.2140/gtm.2009.16.285.

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Versmissen, Koen. "Categorial grammar, modalities and algebraic semantics." In the sixth conference. Association for Computational Linguistics, 1993. http://dx.doi.org/10.3115/976744.976788.

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Yue, Xiaowei. "Data Decomposition for Analytics of Engineering Systems: Literature Review, Methodology Formulation, and Future Trends." In ASME 2019 14th International Manufacturing Science and Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/msec2019-2945.

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Abstract Data decomposition is an important step for high-dimensional data analytics of complex engineering systems, but it is less emphasized in our current data analytics domain. This paper summarizes the key techniques for data decomposition, and separates them into two categories. One is deterministic decomposition, and the other is stochastic decomposition. The deterministic decomposition captures geometric or algebraic shape from the high-dimensional datasets directly, which is efficient for feature extraction and dimensionality reduction; while the stochastic decomposition provides prob

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