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Journal articles on the topic 'Semi-abelian categorie'

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Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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1

Janelidze, George, László Márki, and Walter Tholen. "Semi-abelian categories." Journal of Pure and Applied Algebra 168, no. 2-3 (March 2002): 367–86. http://dx.doi.org/10.1016/s0022-4049(01)00103-7.

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2

Janelidze, Tamar. "Relative Semi-abelian Categories." Applied Categorical Structures 17, no. 4 (August 12, 2008): 373–86. http://dx.doi.org/10.1007/s10485-008-9155-2.

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3

Gran, Marino, and Stephen Lack. "Semi-localizations of semi-abelian categories." Journal of Algebra 454 (May 2016): 206–32. http://dx.doi.org/10.1016/j.jalgebra.2016.01.024.

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4

Janelidze, Tamar. "Incomplete Relative Semi-Abelian Categories." Applied Categorical Structures 19, no. 1 (March 17, 2009): 257–70. http://dx.doi.org/10.1007/s10485-009-9193-4.

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5

Bourn, Dominique, and Marino Gran. "Central extensions in semi-abelian categories." Journal of Pure and Applied Algebra 175, no. 1-3 (November 2002): 31–44. http://dx.doi.org/10.1016/s0022-4049(02)00127-5.

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6

der Linden, Tim Van. "Simplicial homotopy in semi-abelian categories." Journal of K-Theory 4, no. 2 (September 4, 2008): 379–90. http://dx.doi.org/10.1017/is008008022jkt070.

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AbstractWe study Quillen's model category structure for homotopy of simplicial objects in the context of Janelidze, Márki and Tholen's semi-abelian categories. This model structure exists as soon as is regular Mal'tsev and has enough regular projectives; then the fibrations are the Kan fibrations of S. When, moreover, is semi-abelian, weak equivalences and homology isomorphisms coincide.

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7

di Micco, Davide, and Tim Van der Linden. "Compatible actions in semi-abelian categories." Homology, Homotopy and Applications 22, no. 2 (2020): 221–50. http://dx.doi.org/10.4310/hha.2020.v22.n2.a14.

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8

Gran, Marino, George Janelidze, and Aldo Ursini. "Weighted commutators in semi-abelian categories." Journal of Algebra 397 (January 2014): 643–65. http://dx.doi.org/10.1016/j.jalgebra.2013.07.037.

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9

Goedecke, Julia. "Homology in Relative Semi-Abelian Categories." Applied Categorical Structures 21, no. 6 (May 5, 2012): 523–43. http://dx.doi.org/10.1007/s10485-012-9278-3.

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10

Everaert, Tomas, and Tim Van der Linden. "Relative commutator theory in semi-abelian categories." Journal of Pure and Applied Algebra 216, no. 8-9 (August 2012): 1791–806. http://dx.doi.org/10.1016/j.jpaa.2012.02.018.

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11

Casas, José Manuel, and Tim Van der Linden. "Universal Central Extensions in Semi-Abelian Categories." Applied Categorical Structures 22, no. 1 (March 20, 2013): 253–68. http://dx.doi.org/10.1007/s10485-013-9304-0.

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12

Kopylov, Yaroslav A. "On Some Diagram Assertions in Preabelian and P-Semi-Abelian Categories." Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 20, no. 4 (2020): 434–43. http://dx.doi.org/10.18500/1816-9791-2020-20-4-434-443.

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As is well known, many important additive categories in functional analysis and algebra are not abelian. Many classical diagram assertions valid in abelian categories fail in more general additive categories without additional assumptions concerning the properties of the morphisms of the diagrams under consideration. This in particular applies to the so-called Snake Lemma, or the KerCoker-sequence. We obtain a theorem about a diagram generalizing the classical situation of the Snake Lemma in the context of categories semi-abelian in the sense of Palamodov. It is also known that, already in P-semi-abelian categories, not all kernels (respectively, cokernels) are semi-stable, that is, stable under pushouts (respectively, pullbacks). We prove a proposition showing how non-semi-stable kernels and cokernels can arise in general preabelian categories.

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13

Gray, J. R. A. "Hall's criterion for nilpotence in semi-abelian categories." Advances in Mathematics 349 (June 2019): 911–19. http://dx.doi.org/10.1016/j.aim.2019.04.025.

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14

Janelidze, George. "Frattini Subobjects and Extensions in Semi-Abelian Categories." Bulletin of the Iranian Mathematical Society 44, no. 2 (February 28, 2018): 291–304. http://dx.doi.org/10.1007/s41980-018-0020-2.

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15

Xin, L. Y. Chen and L. "One-Side Derived Categories of Pre-Strict P-Semi-Abelian Categories." Journal of Mathematical Study 48, no. 4 (June 2015): 406–18. http://dx.doi.org/10.4208/jms.v48n4.15.07.

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16

GOEDECKE, JULIA, and TIM VAN DER LINDEN. "On satellites in semi-abelian categories: Homology without projectives." Mathematical Proceedings of the Cambridge Philosophical Society 147, no. 3 (June 22, 2009): 629–57. http://dx.doi.org/10.1017/s0305004109990107.

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AbstractWorking in a semi-abelian context, we use Janelidze's theory of generalised satellites to study universal properties of the Everaert long exact homology sequence. This results in a new definition of homology which does not depend on the existence of projective objects. We explore the relations with other notions of homology, and thus prove a version of the higher Hopf formulae. We also work out some examples.

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17

Gran, Marino, and Tim Van der Linden. "On the second cohomology group in semi-abelian categories." Journal of Pure and Applied Algebra 212, no. 3 (March 2008): 636–51. http://dx.doi.org/10.1016/j.jpaa.2007.06.009.

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18

Gray, J. R. A. "Normalizers, Centralizers and Action Representability in Semi-Abelian Categories." Applied Categorical Structures 22, no. 5-6 (October 2014): 981–1007. http://dx.doi.org/10.1007/s10485-014-9379-2.

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19

Kopylov, Ya A. "The five- and nine-lemmas in P-semi-abelian categories." Siberian Mathematical Journal 50, no. 5 (September 2009): 867–73. http://dx.doi.org/10.1007/s11202-009-0097-1.

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20

Goswami, Amartya. "Salamander lemma for non-abelian group-like structures." Journal of Algebra and Its Applications 19, no. 02 (March 15, 2019): 2050022. http://dx.doi.org/10.1142/s021949882050022x.

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It is well known that the classical diagram lemmas of homological algebra for abelian groups can be generalized to non-abelian group-like structures, such as groups, rings, algebras, loops, etc. In this paper, we establish such a generalization of the “salamander lemma” due to G. M. Bergman, in a self-dual axiomatic context (developed originally by Z. Janelidze), which applies to all usual non-abelian group-like structures and also covers axiomatic contexts such as semi-abelian categories in the sense of G. Janelidze, L. Márki and W. Tholen and exact categories in the sense of M. Grandis.

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21

Liu, Heguo, Xingzhong Xu, and Jiping Zhang. "A bound for Hall's criterion for nilpotence in semi-abelian categories." Journal of Algebra 566 (January 2021): 302–8. http://dx.doi.org/10.1016/j.jalgebra.2020.09.006.

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22

Janelidze, G., L. Márki, and A. Ursini. "Ideals and clots in universal algebra and in semi-abelian categories." Journal of Algebra 307, no. 1 (January 2007): 191–208. http://dx.doi.org/10.1016/j.jalgebra.2006.05.022.

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23

Janelidze-Gray, Tamar. "Composites of Central Extensions Form a Relative Semi-Abelian Category." Applied Categorical Structures 22, no. 5-6 (December 4, 2013): 857–72. http://dx.doi.org/10.1007/s10485-013-9354-3.

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24

SCHÄPPI, DANIEL. "Ind-abelian categories and quasi-coherent sheaves." Mathematical Proceedings of the Cambridge Philosophical Society 157, no. 3 (October 2, 2014): 391–423. http://dx.doi.org/10.1017/s0305004114000401.

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AbstractWe study the question of when a category of ind-objects is abelian. Our answer allows a further generalization of the notion of weakly Tannakian categories introduced by the author. As an application we show that, under suitable conditions, the category of coherent sheaves on the product of two schemes with the resolution property is given by the Deligne tensor product of the categories of coherent sheaves of the two factors. To do this we prove that the class of quasi-compact and semi-separated schemes with the resolution property is closed under fiber products.

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25

Janelidze, Zurab. "On the Form of Subobjects in Semi-Abelian and Regular Protomodular Categories." Applied Categorical Structures 22, no. 5-6 (December 5, 2013): 755–66. http://dx.doi.org/10.1007/s10485-013-9355-2.

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26

Kopylov, Yaroslav, and Sven-Ake Wegner. "On the Notion of a Semi-Abelian Category in the Sense of Palamodov." Applied Categorical Structures 20, no. 5 (March 25, 2011): 531–41. http://dx.doi.org/10.1007/s10485-011-9249-0.

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27

Bezrukavnikov, Roman, Alexander Braverman, and Leonid Positselskii. "GLUING OF ABELIAN CATEGORIES AND DIFFERENTIAL OPERATORS ON THE BASIC AFFINE SPACE." Journal of the Institute of Mathematics of Jussieu 1, no. 4 (October 2002): 543–57. http://dx.doi.org/10.1017/s1474748002000154.

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The notion of gluing of abelian categories was introduced in a paper by Kazhdan and Laumon in 1988 and studied further by Polishchuk. We observe that this notion is a particular case of a general categorical construction.We then apply this general notion to the study of the ring of global differential operators $\mathcal{D}$ on the basic affine space $G/U$ (here $G$ is a semi-simple simply connected algebraic group over $\mathbb{C}$ and $U\subset G$ is a maximal unipotent subgroup).We show that the category of $\mathcal{D}$-modules is glued from $|W|$ copies of the category of $D$-modules on $G/U$ where $W$ is the Weyl group, and the Fourier transform is used to define the gluing data. As an application we prove that the algebra $\mathcal{D}$ is Noetherian, and get some information on its homological properties.AMS 2000 Mathematics subject classification: Primary 13N10; 16S32; 17B10; 18C20

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