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Journal articles on the topic 'Quasi-categories'

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Published: 10 December 2022
Last updated: 29 January 2023

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1

Harpaz, Yonatan. "Quasi-unital ∞–categories." Algebraic & Geometric Topology 15, no. 4 (September 10, 2015): 2303–81. http://dx.doi.org/10.2140/agt.2015.15.2303.

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2

Zhao, Deke. "Skew categories, smash product categories and quasi-Koszul categories." Proceedings of the American Mathematical Society 139, no. 08 (August 1, 2011): 2657. http://dx.doi.org/10.1090/s0002-9939-2011-10695-6.

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3

Dugger, Daniel, and David I. Spivak. "Rigidification of quasi-categories." Algebraic & Geometric Topology 11, no. 1 (January 7, 2011): 225–61. http://dx.doi.org/10.2140/agt.2011.11.225.

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4

Steimle, Wolfgang. "Degeneracies in quasi-categories." Journal of Homotopy and Related Structures 13, no. 4 (February 24, 2018): 703–14. http://dx.doi.org/10.1007/s40062-018-0199-1.

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5

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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6

Dugger, Daniel, and David I. Spivak. "Mapping spaces in quasi-categories." Algebraic & Geometric Topology 11, no. 1 (January 7, 2011): 263–325. http://dx.doi.org/10.2140/agt.2011.11.263.

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7

Joyal, A. "Quasi-categories and Kan complexes." Journal of Pure and Applied Algebra 175, no. 1-3 (November 2002): 207–22. http://dx.doi.org/10.1016/s0022-4049(02)00135-4.

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8

RIEHL, EMILY. "On the structure of simplicial categories associated to quasi-categories." Mathematical Proceedings of the Cambridge Philosophical Society 150, no. 3 (March 11, 2011): 489–504. http://dx.doi.org/10.1017/s0305004111000053.

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AbstractThe homotopy coherent nerve from simplicial categories to simplicial sets and its left adjoint are important to the study of (∞, 1)-categories because they provide a means for comparing two models of their respective homotopy theories, giving a Quillen equivalence between the model structures for quasi-categories and simplicial categories. The functor also gives a cofibrant replacement for ordinary categories, regarded as trivial simplicial categories. However, the hom-spaces of the simplicial category X arising from a quasi-category X are not well understood. We show that when X is a quasi-category, all Λ21 horns in the hom-spaces of its simplicial category can be filled. We prove, unexpectedly, that for any simplicial set X, the hom-spaces of X are 3-coskeletal. We characterize the quasi-categories whose simplicial categories are locally quasi, finding explicit examples of 3-dimensional horns that cannot be filled in all other cases. Finally, we show that when X is the nerve of an ordinary category, X is isomorphic to the simplicial category obtained from the standard free simplicial resolution, showing that the two known cofibrant “simplicial thickenings” of ordinary categories coincide, and furthermore its hom-spaces are 2-coskeletal.
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9

Maehara, Yuki. "Inner horns for 2-quasi-categories." Advances in Mathematics 363 (March 2020): 107003. http://dx.doi.org/10.1016/j.aim.2020.107003.

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10

Schmitt, Vincent. "Enriched Categories and Quasi-uniform Spaces." Electronic Notes in Theoretical Computer Science 73 (October 2004): 165–205. http://dx.doi.org/10.1016/j.entcs.2004.08.009.

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11

Bauch, Manfred. "Subspace categories as categories of good modules over quasi-hereditary algebras." Archiv der Mathematik 62, no. 2 (February 1994): 112–15. http://dx.doi.org/10.1007/bf01198665.

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12

Ara, Dimitri. "Higher Quasi-Categories vs Higher Rezk Spaces." Journal of K-theory 14, no. 3 (December 2014): 701–49. http://dx.doi.org/10.1017/s1865243315000021.

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AbstractWe introduce a notion of n-quasi-categories as fibrant objects of a model category structure on presheaves on Joyal's n-cell category Θn. Our definition comes from an idea of Cisinski and Joyal. However, we show that this idea has to be slightly modified to get a reasonable notion. We construct two Quillen equivalences between the model category of n-quasi-categories and the model category of Rezk Θn-spaces, showing that n-quasi-categories are a model for (∞, n)-categories. For n = 1, we recover the two Quillen equivalences defined by Joyal and Tierney between quasi-categories and complete Segal spaces.
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13

Pauwels, Bregje. "Quasi-Galois theory in symmetric monoidal categories." Algebra & Number Theory 11, no. 8 (October 15, 2017): 1891–920. http://dx.doi.org/10.2140/ant.2017.11.1891.

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14

Aksyutina, Z. A. "Categories of social and quasi-social education." Bulletin of Chelyabinsk State University, no. 11 (2021): 54–65. http://dx.doi.org/10.47475/1994-2796-2021-11108.

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15

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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16

Riehl, Emily, and Dominic Verity. "The 2-category theory of quasi-categories." Advances in Mathematics 280 (August 2015): 549–642. http://dx.doi.org/10.1016/j.aim.2015.04.021.

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17

Hanamura, Masaki. "Quasi DG categories and mixed motivic sheaves." Journal of Pure and Applied Algebra 219, no. 7 (July 2015): 2816–900. http://dx.doi.org/10.1016/j.jpaa.2014.09.030.

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18

Holgate, David, and Minani Iragi. "Quasi-uniform and syntopogenous structures on categories." Topology and its Applications 263 (August 2019): 16–25. http://dx.doi.org/10.1016/j.topol.2019.05.024.

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19

Bulacu, D., S. Caenepeel, and F. Panaite. "Yetter-Drinfeld Categories for Quasi-Hopf Algebras." Communications in Algebra 34, no. 1 (January 2006): 1–35. http://dx.doi.org/10.1080/00927870500345869.

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20

Genovese, Francesco. "Adjunctions of Quasi-Functors Between DG-Categories." Applied Categorical Structures 25, no. 4 (November 7, 2016): 625–57. http://dx.doi.org/10.1007/s10485-016-9470-y.

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21

Femić, Bojana. "Eilenberg–Watts Theorem for 2-categories and quasi-monoidal structures for module categories over bialgebroid categories." Journal of Pure and Applied Algebra 220, no. 9 (September 2016): 3156–81. http://dx.doi.org/10.1016/j.jpaa.2016.02.009.

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22

Sakáloš, Štefan. "On categories associated to a Quasi-Hopf algebra." Communications in Algebra 45, no. 2 (October 7, 2016): 722–48. http://dx.doi.org/10.1080/00927872.2016.1175449.

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23

Kapulkin, Krzysztof. "Locally cartesian closed quasi‐categories from type theory." Journal of Topology 10, no. 4 (November 6, 2017): 1029–49. http://dx.doi.org/10.1112/topo.12031.

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24

Maehara, Yuki. "The Gray tensor product for 2-quasi-categories." Advances in Mathematics 377 (January 2021): 107461. http://dx.doi.org/10.1016/j.aim.2020.107461.

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25

Huang, Hua-Lin, Gongxiang Liu, and Yu Ye. "Quivers, Quasi-Quantum Groups and Finite Tensor Categories." Communications in Mathematical Physics 303, no. 3 (March 27, 2011): 595–612. http://dx.doi.org/10.1007/s00220-011-1229-6.

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26

Kodjabachev, Dimitar, and Steffen Sagave. "Strictly commutative models for $E_\infty$ quasi-categories." Homology, Homotopy and Applications 17, no. 1 (2015): 121–28. http://dx.doi.org/10.4310/hha.2015.v17.n1.a5.

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27

Brandenburg, Martin, and Alexandru Chirvasitu. "Tensor functors between categories of quasi-coherent sheaves." Journal of Algebra 399 (February 2014): 675–92. http://dx.doi.org/10.1016/j.jalgebra.2013.09.050.

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28

Dikranjan, Dikran, and Hans-Peter A. Künzi. "Cowellpoweredness of Some Categories of Quasi-Uniform Spaces." Applied Categorical Structures 26, no. 6 (April 7, 2018): 1159–84. http://dx.doi.org/10.1007/s10485-018-9523-5.

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29

Hu, Hongde, and Walter Tholen. "Quasi-coproducts and accessible categories with wide pullbacks." Applied Categorical Structures 4, no. 4 (December 1996): 387–402. http://dx.doi.org/10.1007/bf00122686.

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30

ALVARES, E. R., I. ASSEM, F. U. COELHO, M. I. PEÑA, and S. TREPODE. "FROM TRISECTIONS IN MODULE CATEGORIES TO QUASI-DIRECTED COMPONENTS." Journal of Algebra and Its Applications 10, no. 03 (June 2011): 409–33. http://dx.doi.org/10.1142/s0219498811004653.

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In this paper, we define and study a special type of trisections in a module category, namely the compact trisections which characterize quasi-directed components. We apply this notion to the study of laura algebras and we use it to define a class of algebras with predictable Auslander–Reiten components.
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31

Tahata, Kouji. "Quasi-asymmetry model for square tables with nominal categories." Journal of Applied Statistics 39, no. 4 (April 2012): 723–29. http://dx.doi.org/10.1080/02664763.2011.610447.

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32

Ortiz-Morales, Martín. "The Auslander–Reiten Components Seen as Quasi-Hereditary Categories." Applied Categorical Structures 26, no. 2 (May 10, 2017): 239–85. http://dx.doi.org/10.1007/s10485-017-9493-z.

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33

Fiorot, Luisa. "$n$-quasi-abelian categories vs $n$-tilting torsion pairs." Documenta Mathematica 26 (2021): 149–97. http://dx.doi.org/10.4171/dm/812.

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34

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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35

Fujisawa, Kengo, and Kouji Tahata. "Quasi Association Models for Square Contingency Tables with Ordinal Categories." Symmetry 14, no. 4 (April 12, 2022): 805. http://dx.doi.org/10.3390/sym14040805.

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The analysis of contingency tables focuses on a statistical model instead of independence when the independence between row and column variables does not hold. Many association models have been proposed to indicate the structure of odds ratios. Additionally, symmetry and asymmetry models have been proposed to analyze the cell probabilities of square contingency tables with symmetric or asymmetric structures. This paper proposes an asymmetry plus association model for square contingency tables with ordinal categories and partitioning of the test statistic for goodness-of-fit using our proposed model.
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36

Liu, Shaoxue, and Changchang Xi. "Quadratic forms for △–good module categories of quasi-Hereditary algebras." Communications in Algebra 27, no. 8 (January 1999): 3719–25. http://dx.doi.org/10.1080/00927879908826658.

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37

Shah, Amit. "Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categories." Journal of Pure and Applied Algebra 224, no. 1 (January 2020): 98–124. http://dx.doi.org/10.1016/j.jpaa.2019.04.017.

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38

Shah, Amit. "Quasi-abelian hearts of twin cotorsion pairs on triangulated categories." Journal of Algebra 534 (September 2019): 313–38. http://dx.doi.org/10.1016/j.jalgebra.2019.06.011.

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39

Koenig, Steffen, Julian Külshammer, and Sergiy Ovsienko. "Quasi-hereditary algebras, exact Borel subalgebras,A∞-categories and boxes." Advances in Mathematics 262 (September 2014): 546–92. http://dx.doi.org/10.1016/j.aim.2014.05.016.

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40

Dikranjan, Dikran, and Nicolò Zava. "Categories of coarse groups: Quasi-homomorphisms and functorial coarse structures." Topology and its Applications 273 (March 2020): 106980. http://dx.doi.org/10.1016/j.topol.2019.106980.

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41

KOSTANEK, MATEUSZ, and PAWEŁ WASZKIEWICZ. "The formal ball model for -categories." Mathematical Structures in Computer Science 21, no. 1 (December 2, 2010): 41–64. http://dx.doi.org/10.1017/s0960129510000447.

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We generalise the construction of the formal ball model for metric spaces due to A. Edalat and R. Heckmann in order to obtain computational models for separated-categories. We fully describe-categories that are(a)Yoneda complete(b)continuous Yoneda completevia their formal ball models. Our results yield solutions to two open problems in the theory of quasi-metric spaces by showing that:(a)a quasi-metric spaceXis Yoneda complete if and only if its formal ball model is a dcpo, and(b)a quasi-metric spaceXis continuous and Yoneda complete if and only if its formal ball modelBXis a domain that admits a simple characterisation of approximation.
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42

Hall, Jack, and David Rydh. "Perfect complexes on algebraic stacks." Compositio Mathematica 153, no. 11 (August 17, 2017): 2318–67. http://dx.doi.org/10.1112/s0010437x17007394.

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We develop a theory of unbounded derived categories of quasi-coherent sheaves on algebraic stacks. In particular, we show that these categories are compactly generated by perfect complexes for stacks that either have finite stabilizers or are local quotient stacks. We also extend Toën and Antieau–Gepner’s results on derived Azumaya algebras and compact generation of sheaves on linear categories from derived schemes to derived Deligne–Mumford stacks. These are all consequences of our main theorem: compact generation of a presheaf of triangulated categories on an algebraic stack is local for the quasi-finite flat topology.
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43

HOLSTEIN, JULIAN V. S. "Morita cohomology." Mathematical Proceedings of the Cambridge Philosophical Society 158, no. 1 (December 5, 2014): 1–26. http://dx.doi.org/10.1017/s0305004114000516.

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AbstractWe consider two categorifications of the cohomology of a topological spaceXby taking coefficients in the category of differential graded categories. We consider both derived global sections of a constant presheaf and singular cohomology and find the resulting dg-categories are quasi-equivalent and moreover quasi-equivalent to representations in perfect complexes of chains on the loop space ofX.
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44

Hébert, Michel. "Characterizations of Axiomatic Categories of Models Canonically Isomorphic to (Quasi-)Varieties." Canadian Mathematical Bulletin 31, no. 3 (September 1, 1988): 287–300. http://dx.doi.org/10.4153/cmb-1988-042-x.

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AbstractLet be the category of all homomorphisms (i.e. functions preserving satisfaction of atomic formulas) between models of a set of sentences T in a finitary first-order language L. Functors between two such categories are said to be canonical if they commute with the forgetful functors. The following properties are characterized syntactically and also in terms of closure of for some algebraic constructions (involving products, equalizers, factorizations and kernel pairs): There is a canonical isomorphism from to a variety (resp. quasivariety) in a finitary expansion of L which assigns to a model its (unique) expansion. This solves a problem of H. Volger.In the case of a purely algebraic language, the properties are equivalent to:“ is canonically isomorphic to a finitary variety (resp. quasivariety)” and, for the variety case, to “the forgetful functor of is monadic (tripleable)”.
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45

Della Villa, A., V. Galdi, F. Capolino, V. Pierro, S. Enoch, and G. Tayeb. "A Comparative Study of Representative Categories of EBG Dielectric Quasi-Crystals." IEEE Antennas and Wireless Propagation Letters 5 (2006): 331–34. http://dx.doi.org/10.1109/lawp.2006.878904.

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46

Barnes, Gwendolyn E., Alexander Schenkel, and Richard J. Szabo. "Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature." Journal of Geometry and Physics 106 (August 2016): 234–55. http://dx.doi.org/10.1016/j.geomphys.2016.04.005.

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47

Ando, Shuji. "Asymmetry Models Based on Non-integer Scores for Square Contingency Tables." Journal of Statistical Theory and Applications 21, no. 1 (January 25, 2022): 21–30. http://dx.doi.org/10.1007/s44199-022-00039-z.

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AbstractSquare contingency tables with ordinal classifications are used in many disciplines that include but are not limited to data science, engineering, and medical research. This study proposes two original asymmetry models based on non-integer scores for the analysis of square contingency tables. The ordinal quasi-symmetry model applies to data sets that can be assigned to known ordered scores for all categories. When we assign the equally spaced score for categories, the ordinal quasi-symmetry model is equivalent to the linear diagonals-symmetry model. The ordinal quasi-symmetry model, however, is not applicable to data sets that cannot be assigned the known ordered scores for all categories. This study addresses this issue. The proposed models apply to data sets that: (i) can be assigned the known ordered scores for all except one category and (ii) cannot be assigned the known ordered scores for all categories. These two models provide a better fit than existing models for real-world data.
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48

ENOCHS, E., S. ESTRADA, J. R. GARCÍA-ROZAS, and L. OYONARTE. "GENERALIZED QUASI-COHERENT SHEAVES." Journal of Algebra and Its Applications 02, no. 01 (March 2003): 63–83. http://dx.doi.org/10.1142/s0219498803000374.

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The category of quasi-coherent sheaves on the projective line P1(k) (k is a field) is equivalent to certain representations of the quiver • → • ← •. Many of the techniques which are used to study these sheaves apply to more general categories. We give the definitions of these more general categories and then consider one particular such category in depth. In this particular category we prove that there are no (nonzero) projective representations but that the category admits flat covers (or, equivalently in this situation, torsion free covers) and cotorsion envelopes.
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49

Zhang, Xiaohui, and Shuanhong Wang. "New Turaev braided group categories and weak (co)quasi-Turaev group coalgebras." Journal of Mathematical Physics 55, no. 11 (November 2014): 111702. http://dx.doi.org/10.1063/1.4901136.

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50

Iki, Kiyotaka, Kouji Yamamoto, and Sadao Tomizawa. "Quasi-diagonal exponent symmetry model for square contingency tables with ordered categories." Statistics & Probability Letters 92 (September 2014): 33–38. http://dx.doi.org/10.1016/j.spl.2014.04.029.

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