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Journal articles on the topic 'Categorías abelianas'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Pop, Flaviu. "Coplexes in abelian categories." Studia Universitatis Babes-Bolyai Matematica 62, no. 1 (March 1, 2017): 3–13. http://dx.doi.org/10.24193/subbmath.2017.0001.

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2

Ebrahimi, Ramin, and Alireza Nasr-Isfahani. "Representation of n-abelian categories in abelian categories." Journal of Algebra 563 (December 2020): 352–75. http://dx.doi.org/10.1016/j.jalgebra.2020.07.010.

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3

ZHENG, QILIAN, and JIAQUN WEI. "QUOTIENT CATEGORIES OF n-ABELIAN CATEGORIES." Glasgow Mathematical Journal 62, no. 3 (September 30, 2019): 673–705. http://dx.doi.org/10.1017/s0017089519000417.

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AbstractThe notion of mutation pairs of subcategories in an n-abelian category is defined in this paper. Let ${\cal D} \subseteq {\cal Z}$ be subcategories of an n-abelian category ${\cal A}$. Then the quotient category ${\cal Z}/{\cal D}$ carries naturally an (n + 2) -angulated structure whenever $ ({\cal Z},{\cal Z}) $ forms a ${\cal D} \subseteq {\cal Z}$-mutation pair and ${\cal Z}$ is extension-closed. Moreover, we introduce strongly functorially finite subcategories of n-abelian categories and show that the corresponding quotient categories are one-sided (n + 2)-angulated categories. Finally, we study homological finiteness of subcategories in a mutation pair.

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4

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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5

Lyubashenko, V. "Ribbon Abelian Categories as Modular Categories." Journal of Knot Theory and Its Ramifications 05, no. 03 (June 1996): 311–403. http://dx.doi.org/10.1142/s0218216596000229.

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A category N of labeled (oriented) trivalent graphs (nets) or ribbon graphs is extended by new generators called fusing, braiding, twist and switch with relations which can be called Moore-Seiberg relations. A functor to N is constructed from the category Surf of oriented surfaces with labeled boundary and their homeomorphisms. Given a (eventually non-semisimple) k-linear abelian ribbon braided category [Formula: see text] with some finiteness conditions we construct a functor from a central extension of N with the set of labels [Formula: see text] ObC to k-vector spaces. Composing the functors we get a modular functor from a central extension of Surfto k-vector spaces.

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6

Gillespie, James. "Hereditary abelian model categories." Bulletin of the London Mathematical Society 48, no. 6 (September 13, 2016): 895–922. http://dx.doi.org/10.1112/blms/bdw051.

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7

Chen, Xiao-Wu, and Henning Krause. "Expansions of abelian categories." Journal of Pure and Applied Algebra 215, no. 12 (December 2011): 2873–83. http://dx.doi.org/10.1016/j.jpaa.2011.04.008.

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8

Kato, Toyonori, and Tamotsu Ikeyama. "Localization in Abelian Categories." Communications in Algebra 18, no. 8 (January 1990): 2519–40. http://dx.doi.org/10.1080/00927879008824036.

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9

Richman, Fred. "Pre-abelian Clan Categories." Rocky Mountain Journal of Mathematics 32, no. 4 (December 2002): 1605–16. http://dx.doi.org/10.1216/rmjm/1181070043.

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10

Zhou, Panyue, and Bin Zhu. "n-Abelian quotient categories." Journal of Algebra 527 (June 2019): 264–79. http://dx.doi.org/10.1016/j.jalgebra.2019.03.007.

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11

Kálnai, Peter, and Jan Žemlička. "Compactness in abelian categories." Journal of Algebra 534 (September 2019): 273–88. http://dx.doi.org/10.1016/j.jalgebra.2019.05.037.

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12

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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13

Amzil, Houda, Driss Bennis, J. R. García Rozas, Hanane Ouberka, and Luis Oyonarte. "Subprojectivity in Abelian Categories." Applied Categorical Structures 29, no. 5 (March 11, 2021): 889–913. http://dx.doi.org/10.1007/s10485-021-09638-w.

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14

Zhou, Panyue, Jinde Xu, and Baiyu Ouyang. "Mutation pairs and quotient categories of Abelian categories." Communications in Algebra 45, no. 1 (October 11, 2016): 392–410. http://dx.doi.org/10.1080/00927872.2016.1175581.

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15

Liu, Yu, and Panyue Zhou. "From n-exangulated categories to n-abelian categories." Journal of Algebra 579 (August 2021): 210–30. http://dx.doi.org/10.1016/j.jalgebra.2021.03.029.

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16

Pop, Flaviu. "Natural dualities between abelian categories." Central European Journal of Mathematics 9, no. 5 (May 26, 2011): 1088–99. http://dx.doi.org/10.2478/s11533-011-0048-5.

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17

Schneiders, Jean-Pierre. "Quasi-abelian categories and sheaves." Mémoires de la Société mathématique de France 1 (1999): 1–140. http://dx.doi.org/10.24033/msmf.389.

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18

Lowen, Wendy, and Michel Van den Bergh. "Deformation theory of abelian categories." Transactions of the American Mathematical Society 358, no. 12 (December 1, 2006): 5441–84. http://dx.doi.org/10.1090/s0002-9947-06-03871-2.

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19

Xu, Jinde, Panyue Zhou, and Baiyu Ouyang. "Mutation Pairs in Abelian Categories." Communications in Algebra 44, no. 7 (June 2016): 2732–46. http://dx.doi.org/10.1080/00927872.2015.1053900.

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20

Sather-Wagstaff, Sean, Tirdad Sharif, and Diana White. "Gorenstein cohomology in abelian categories." Journal of Mathematics of Kyoto University 48, no. 3 (2008): 571–96. http://dx.doi.org/10.1215/kjm/1250271384.

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21

Gentle, Ronald. "T.T.F. theories in abelian categories." Communications in Algebra 16, no. 5 (January 1988): 877–908. http://dx.doi.org/10.1080/00927878808823609.

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22

Baues, Hans-Joachim, and Mamuka Jibladze. "Classification of Abelian Track Categories." K-Theory 25, no. 3 (March 2002): 299–311. http://dx.doi.org/10.1023/a:1015607114629.

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23

Crivei, Septimiu, M. Tamer Koşan, and Tülay Yildirim. "Regular morphisms in abelian categories." Journal of Algebra and Its Applications 18, no. 09 (July 17, 2019): 1950180. http://dx.doi.org/10.1142/s0219498819501809.

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We establish some properties involving regular morphisms in abelian categories. We show a decomposition theorem on the image of a regular sum of morphisms, a characterization of regular morphisms in terms of consecutive pairs of morphisms, and a description of certain equivalent morphisms. We also generalize Ehrlich’s Theorem on one-sided unit regular morphisms by showing that if [Formula: see text] is an [Formula: see text]-regular object, then a morphism [Formula: see text] is left (right) unit regular if and only if there exists a split monomorphism (epimorphism) [Formula: see text]. We also study regular morphisms determined by generalized inverses in additive categories.

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24

Mozgovoy, Sergey. "Quiver representations in abelian categories." Journal of Algebra 541 (January 2020): 35–50. http://dx.doi.org/10.1016/j.jalgebra.2019.08.027.

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25

Becerril, Víctor, Octavio Mendoza, Marco A. Pérez, and Valente Santiago. "Frobenius pairs in abelian categories." Journal of Homotopy and Related Structures 14, no. 1 (May 17, 2018): 1–50. http://dx.doi.org/10.1007/s40062-018-0208-4.

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26

Grimeland, Benedikte, and Karin Marie Jacobsen. "Abelian quotients of triangulated categories." Journal of Algebra 439 (October 2015): 110–33. http://dx.doi.org/10.1016/j.jalgebra.2015.04.042.

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27

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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28

Kvamme, Sondre. "Axiomatizing subcategories of Abelian categories." Journal of Pure and Applied Algebra 226, no. 4 (April 2022): 106862. http://dx.doi.org/10.1016/j.jpaa.2021.106862.

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29

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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30

Entova-Aizenbud, Inna, Vladimir Hinich, and Vera Serganova. "Deligne Categories and the Limit of Categories Rep(GL(m|n))." International Mathematics Research Notices 2020, no. 15 (June 27, 2018): 4602–66. http://dx.doi.org/10.1093/imrn/rny144.

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Abstract For each integer $t$ a tensor category $\mathcal{V}_t$ is constructed, such that exact tensor functors $\mathcal{V}_t\rightarrow \mathcal{C}$ classify dualizable $t$-dimensional objects in $\mathcal{C}$ not annihilated by any Schur functor. This means that $\mathcal{V}_t$ is the “abelian envelope” of the Deligne category $\mathcal{D}_t=\operatorname{Rep}(GL_t)$. Any tensor functor $\operatorname{Rep}(GL_t)\longrightarrow \mathcal{C}$ is proved to factor either through $\mathcal{V}_t$ or through one of the classical categories $\operatorname{Rep}(GL(m|n))$ with $m-n=t$. The universal property of $\mathcal{V}_t$ implies that it is equivalent to the categories $\operatorname{Rep}_{\mathcal{D}_{t_1}\otimes \mathcal{D}_{t_2}}(GL(X),\epsilon )$, ($t=t_1+t_2$, $t_1$ not an integer) suggested by Deligne as candidates for the role of abelian envelope.

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31

Rump, Wolfgang. "Flat covers in abelian and in non-abelian categories." Advances in Mathematics 225, no. 3 (October 2010): 1589–615. http://dx.doi.org/10.1016/j.aim.2010.03.027.

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32

Lin, Zengqiang, and Yang Zhang. "Subquotients of one-sided triangulated categories by rigid subcategories as module categories." Journal of Algebra and Its Applications 14, no. 07 (April 24, 2015): 1550104. http://dx.doi.org/10.1142/s0219498815501042.

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We prove that certain subquotient categories of one-sided triangulated categories are module categories, and in some cases, they are abelian. This unifies a result by Koenig–Zhu for triangulated categories and a result by Demonet–Liu for exact categories.

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33

Lin, YaNan, and MinXiong Wang. "From recollement of triangulated categories to recollement of abelian categories." Science China Mathematics 53, no. 4 (March 20, 2010): 1111–16. http://dx.doi.org/10.1007/s11425-009-0189-1.

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34

Chen, Qing-hua, and Min Zheng. "Recollements of abelian categories and special types of comma categories." Journal of Algebra 321, no. 9 (May 2009): 2474–85. http://dx.doi.org/10.1016/j.jalgebra.2009.01.025.

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35

Positselski, Leonid, and Jan Šťovíček. "Derived, coderived, and contraderived categories of locally presentable abelian categories." Journal of Pure and Applied Algebra 226, no. 4 (April 2022): 106883. http://dx.doi.org/10.1016/j.jpaa.2021.106883.

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36

Huybrechts, Daniel, Emanuele Macrì, and Paolo Stellari. "Stability conditions for generic K3 categories." Compositio Mathematica 144, no. 1 (January 2008): 134–62. http://dx.doi.org/10.1112/s0010437x07003065.

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AbstractA K3 category is by definition a Calabi–Yau category of dimension two. Geometrically K3 categories occur as bounded derived categories of (twisted) coherent sheaves on K3 or abelian surfaces. A K3 category is generic if there are no spherical objects (or just one up to shift). We study stability conditions on K3 categories as introduced by Bridgeland and prove his conjecture about the topology of the stability manifold and the autoequivalences group for generic twisted projective K3, abelian surfaces, and K3 surfaces with trivial Picard group.

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37

Zheng, Junling, Xin Ma, and Zhaoyong Huang. "The Extension Dimension of Abelian Categories." Algebras and Representation Theory 23, no. 3 (February 19, 2019): 693–713. http://dx.doi.org/10.1007/s10468-019-09861-z.

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38

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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39

Parra, Carlos E., and Jorge Vitória. "Properties of abelian categories via recollements." Journal of Pure and Applied Algebra 223, no. 9 (September 2019): 3941–63. http://dx.doi.org/10.1016/j.jpaa.2018.12.013.

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40

Crivei, Septimiu, and Gabriela Olteanu. "Strongly Rickart objects in abelian categories." Communications in Algebra 46, no. 10 (March 8, 2018): 4326–43. http://dx.doi.org/10.1080/00927872.2018.1439046.

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41

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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42

Schäppi, Daniel. "Which abelian tensor categories are geometric?" Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 734 (January 1, 2018): 145–86. http://dx.doi.org/10.1515/crelle-2014-0053.

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AbstractFor a large class of geometric objects, the passage to categories of quasi-coherent sheaves provides an embedding in the 2-category of abelian tensor categories. The notion of weakly Tannakian categories introduced by the author gives a characterization of tensor categories in the image of this embedding.However, this notion requires additional structure to be present, namely a fiber functor. For the case of classical Tannakian categories in characteristic zero, Deligne has found intrinsic properties—expressible entirely within the language of tensor categories—which are necessary and sufficient for the existence of a fiber functor. In this paper we generalize Deligne’s result to weakly Tannakian categories in characteristic zero. The class of geometric objects whose tensor categories of quasi-coherent sheaves can be recognized in this manner includes both the gerbes arising in classical Tannaka duality and more classical geometric objects such as projective varieties over a field of characteristic zero.Our proof uses a different perspective on fiber functors, which we formalize through the notion of geometric tensor categories. A second application of this perspective allows us to describe categories of quasi-coherent sheaves on fiber products.

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43

Rump, Wolfgang. "*-MODULES, TILTING, AND ALMOST ABELIAN CATEGORIES." Communications in Algebra 29, no. 8 (June 30, 2001): 3293–325. http://dx.doi.org/10.1081/agb-100105023.

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44

Becerril, Victor, Octavio Mendoza, and Valente Santiago. "Relative Gorenstein objects in abelian categories." Communications in Algebra 49, no. 1 (September 10, 2020): 352–402. http://dx.doi.org/10.1080/00927872.2020.1800023.

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45

Futorny, Vyacheslav, Marcos Jardim, and Adriano A. Moura. "On Moduli Spaces for Abelian Categories." Communications in Algebra 36, no. 6 (May 27, 2008): 2171–85. http://dx.doi.org/10.1080/00927870801949708.

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46

Jasso, Gustavo. "n-Abelian and n-exact categories." Mathematische Zeitschrift 283, no. 3-4 (January 20, 2016): 703–59. http://dx.doi.org/10.1007/s00209-016-1619-8.

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47

Zhou, Panyue. "A note on abelian quotient categories." Journal of Algebra 551 (June 2020): 1–8. http://dx.doi.org/10.1016/j.jalgebra.2020.01.015.

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48

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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49

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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50

Vallette, Bruno. "Free Monoid in Monoidal Abelian Categories." Applied Categorical Structures 17, no. 1 (March 7, 2008): 43–61. http://dx.doi.org/10.1007/s10485-008-9130-y.

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