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Journal articles on the topic 'Abelian categories'

Author: Grafiati

Published: 4 June 2021

Last updated: 20 February 2023

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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

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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7

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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8

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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9

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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10

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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11

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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12

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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13

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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14

Wu, Yilin, and Guodong Zhou. "From short exact sequences of abelian categories to short exact sequences of homotopy categories and derived categories." Electronic Research Archive 30, no. 2 (2022): 535–64. http://dx.doi.org/10.3934/era.2022028.

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<abstract><p>We show that a short exact sequence of abelian categories gives rise to short exact sequences of abelian categories of complexes, homotopy categories and unbounded derived categories, refining a result of J. Miyachi.</p></abstract>

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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

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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17

Kalebogaz, Berke, and Derya Keskin Tütüncü. "(D4)-Objects in Abelian Categories." Algebra Colloquium 29, no. 02 (April 30, 2022): 231–40. http://dx.doi.org/10.1142/s1005386722000190.

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Let 𝒜 be an abelian category and [Formula: see text]. Then M is called a [Formula: see text]-object if, whenever A and B are subobjects of M with [Formula: see text] and [Formula: see text] is an epimorphism, [Formula: see text] is a direct summand of A. In this paper we give several equivalent conditions of [Formula: see text]-objects in an abelian category. Among other results, we prove that any object M in an abelian category 𝒜 is [Formula: see text] if and only if for every subobject K of M such that K is the intersection [Formula: see text] of perspective direct summands [Formula: see text] and [Formula: see text] of M with [Formula: see text], every morphismr [Formula: see text] can be lifted to an endomorphism [Formula: see text] in [Formula: see text].

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18

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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19

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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20

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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21

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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22

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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23

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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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

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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27

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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28

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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29

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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30

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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31

Franjou, Vincent, and Teimuraz Pirashvili. "Comparison of abelian categories recollements." Documenta Mathematica 9 (2004): 41–56. http://dx.doi.org/10.4171/dm/156.

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32

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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33

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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34

Coulembier, Kevin. "Monoidal abelian envelopes." Compositio Mathematica 157, no. 7 (June 24, 2021): 1584–609. http://dx.doi.org/10.1112/s0010437x21007399.

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We prove a constructive existence theorem for abelian envelopes of non-abelian monoidal categories. This establishes a new tool for the construction of tensor categories. As an example we obtain new proofs for the existence of several universal tensor categories as conjectured by Deligne. Another example constructs interesting tensor categories in positive characteristic via tilting modules for ${\rm SL}_2$.

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35

Gao, Nan, Steffen Koenig, and Chrysostomos Psaroudakis. "Ladders of recollements of abelian categories." Journal of Algebra 579 (August 2021): 256–302. http://dx.doi.org/10.1016/j.jalgebra.2021.02.037.

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36

Chen, Hongxing, and Changchang Xi. "Derived decompositions of abelian categories I." Pacific Journal of Mathematics 312, no. 1 (August 4, 2021): 41–74. http://dx.doi.org/10.2140/pjm.2021.312.41.

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37

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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38

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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39

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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40

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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41

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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42

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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43

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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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

Anh, P. N. "An Embedding Theorem for Abelian Categories." Journal of Algebra 167, no. 3 (August 1994): 627–33. http://dx.doi.org/10.1006/jabr.1994.1205.

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47

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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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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