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Journal articles on the topic 'Small categories'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Baues, Hans-Joachim, and Günther Wirsching. "Cohomology of small categories." Journal of Pure and Applied Algebra 38, no. 2-3 (November 1985): 187–211. http://dx.doi.org/10.1016/0022-4049(85)90008-8.

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2

Noguchi, Kazunori. "Ramified coverings of small categories." Homology, Homotopy and Applications 16, no. 2 (2014): 159–69. http://dx.doi.org/10.4310/hha.2014.v16.n2.a8.

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3

del Hoyo, Matias L. "On the subdivision of small categories." Topology and its Applications 155, no. 11 (June 2008): 1189–200. http://dx.doi.org/10.1016/j.topol.2008.02.006.

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4

Leech, Jonathan. "Constructing inverse monoids from small categories." Semigroup Forum 36, no. 1 (December 1987): 89–116. http://dx.doi.org/10.1007/bf02575008.

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5

Antieau, Benjamin, and Greg Stevenson. "Derived categories of representations of small categories over commutative noetherian rings." Pacific Journal of Mathematics 283, no. 1 (June 14, 2016): 21–42. http://dx.doi.org/10.2140/pjm.2016.283.21.

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6

White, David, and Donald Yau. "Arrow categories of monoidal model categories." MATHEMATICA SCANDINAVICA 125, no. 2 (October 19, 2019): 185–98. http://dx.doi.org/10.7146/math.scand.a-114968.

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We prove that the arrow category of a monoidal model category, equipped with the pushout product monoidal structure and the projective model structure, is a monoidal model category. This answers a question posed by Mark Hovey, in the course of his work on Smith ideals. As a corollary, we prove that the projective model structure in cubical homotopy theory is a monoidal model structure. As illustrations we include numerous examples of non-cofibrantly generated monoidal model categories, including chain complexes, small categories, pro-categories, and topological spaces.

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7

Estrada, Sergio, and Simone Virili. "Cartesian modules over representations of small categories." Advances in Mathematics 310 (April 2017): 557–609. http://dx.doi.org/10.1016/j.aim.2017.01.030.

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8

Xu, Fei. "On the cohomology rings of small categories." Journal of Pure and Applied Algebra 212, no. 11 (November 2008): 2555–69. http://dx.doi.org/10.1016/j.jpaa.2008.04.004.

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9

Tanaka, Kohei. "Čech complexes for covers of small categories." Homology, Homotopy and Applications 19, no. 1 (2017): 281–91. http://dx.doi.org/10.4310/hha.2017.v19.n1.a14.

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10

Hu, Hongde. "Flat functors and free exact categories." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 60, no. 2 (April 1996): 143–56. http://dx.doi.org/10.1017/s1446788700037575.

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AbstractLet C be a small category with weak finite limits, and let Flat(C) be the category of flat functors from C to the category of small sets. We prove that the free exact completion of C is the category of set-valued functors of Flat (C) which preserve small products and filtered colimits. In case C has finite limits, this gives A. Carboni and R. C. Magno's result on the free exact completion of a small category with finite limits.

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11

Luna-Torres, Joaquín. "Filters and compactness on small categories and locales." Open Journal of Mathematical Sciences 6, no. 1 (March 3, 2022): 1–13. http://dx.doi.org/10.30538/oms2022.0174.

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In analogy with the classical theory of filters, for finitely complete or small categories, we provide the concepts of filter, \(\mathfrak{G}\)-neighborhood (short for "Grothendieck-neighborhood") and cover-neighborhood of points of such categories, to study convergence, cluster point, closure of sieves and compactness on objects of that kind of categories. Finally, we study all these concepts in the category \(\mathbf{Loc}\) of locales.

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12

Bagaria, Joan, Carles Casacuberta, A. R. D. Mathias, and Jiří Rosický. "Definable orthogonality classes in accessible categories are small." Journal of the European Mathematical Society 17, no. 3 (2015): 549–89. http://dx.doi.org/10.4171/jems/511.

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13

Gillaspy, Elizabeth, and Alexander Kumjian. "Cohomology for small categories: $k$ -graphs and groupoids." Banach Journal of Mathematical Analysis 12, no. 3 (July 2018): 572–99. http://dx.doi.org/10.1215/17358787-2017-0041.

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14

BENSON, DAVE, SRIKANTH B. IYENGAR, and HENNING KRAUSE. "A local-global principle for small triangulated categories." Mathematical Proceedings of the Cambridge Philosophical Society 158, no. 3 (March 2, 2015): 451–76. http://dx.doi.org/10.1017/s0305004115000067.

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AbstractLocal cohomology functors are constructed for the category of cohomological functors on an essentially small triangulated category ⊺ equipped with an action of a commutative noetherian ring. This is used to establish a local-global principle and to develop a notion of stratification, for ⊺ and the cohomological functors on it, analogous to such concepts for compactly generated triangulated categories.

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15

Xu, Fei. "Hochschild and ordinary cohomology rings of small categories." Advances in Mathematics 219, no. 6 (December 2008): 1872–93. http://dx.doi.org/10.1016/j.aim.2008.07.014.

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16

Raptis, G., and J. Rosický. "Small presentations of model categories and Vopěnka’s principle." Homology, Homotopy and Applications 20, no. 1 (2018): 303–28. http://dx.doi.org/10.4310/hha.2018.v20.n1.a18.

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17

Adámek, J., and J. Reiterman. "Topological categories presented by small sets of axioms." Journal of Pure and Applied Algebra 42, no. 1 (1986): 1–14. http://dx.doi.org/10.1016/0022-4049(86)90054-x.

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18

MacDonald, John, and Laura Scull. "Amalgamations of Categories." Canadian Mathematical Bulletin 52, no. 2 (June 1, 2009): 273–84. http://dx.doi.org/10.4153/cmb-2009-030-5.

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AbstractWe consider the pushout of embedding functors in Cat, the category of small categories. We show that if the embedding functors satisfy a 3-for-2 property, then the induced functors to the pushout category are also embeddings. The result follows from the connectedness of certain associated slice categories. The condition is motivated by a similar result for maps of semigroups. We show that our theorem can be applied to groupoids and to inclusions of full subcategories. We also give an example to show that the theorem does not hold when the property only holds for one of the inclusion functors, or when it is weakened to a one-sided condition.

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19

Breuning, Manuel. "Determinant functors on triangulated categories." Journal of K-Theory 8, no. 2 (July 21, 2010): 251–91. http://dx.doi.org/10.1017/is010006009jkt120.

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AbstractWe study determinant functors which are defined on a triangulated category and take values in a Picard category. The two main results are the existence of a universal determinant functor for every small triangulated category, and a comparison theorem for determinant functors on a triangulated category with a non-degenerate bounded t-structure and determinant functors on its heart. For a small triangulated category Τ we give a natural definition of groups K0(Τ) and K1(Τ) in terms of the universal determinant functor on Τ, and we show that Ki(Τ) ≅ Ki(ε) for i = 0 and 1 if Τ has a non-degenerate bounded t-structure with heart ε.

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20

Börger, Reinhard, and Walter Tholen. "Total Categories and Solid Functors." Canadian Journal of Mathematics 42, no. 2 (April 1, 1990): 213–29. http://dx.doi.org/10.4153/cjm-1990-012-x.

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Totality of a category as introduced by Street and Walters [17] is known to be a strong cocompleteness property (cf. also [21]) which goes far beyond ordinary (small) cocompleteness. It implies compactness in the sense of Isbell [11] and therefore hypercompleteness [7], that is: the existence of limits of all those (not necessarily small) diagrams which are not prevented from having a limit merely from size-considerations with respect to the homsets. In particular, arbitrary intersections of monomorphisms exist in a total category; which is part of Street's [16] characterization of totality and is used in establishing the interrelationship with topoi (cf. also [15]).

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21

Borceux, Francis, and Carmen Quinteriro. "Enriched accessible categories." Bulletin of the Australian Mathematical Society 54, no. 3 (December 1996): 489–501. http://dx.doi.org/10.1017/s0004972700021900.

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We consider category theory enriched in a locally finitely presentable symmetric monoidal closed category ν. We define the ν-filtered colimits as those colimits weighted by a ν-flat presheaf and consider the corresponding notion of ν-accessible category. We prove that ν-accessible categories coincide with the categories of ν-flat presheaves and also with the categories of ν-points of the categories of ν-presheaves. Moreover, the ν-locally finitely presentable categories are exactly the ν-cocomplete finitely accessible ones. To prove this last result, we show that the Cauchy completion of a small ν-category Cis equivalent to the category of ν-finitely presentable ν-flat presheaves on C.

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22

Shoikhet, Boris. "On the twisted tensor product of small dg categories." Journal of Noncommutative Geometry 14, no. 2 (July 29, 2020): 789–820. http://dx.doi.org/10.4171/jncg/380.

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23

Fiore, Thomas M., Simona Paoli, and Dorette Pronk. "Model structures on the category of small double categories." Algebraic & Geometric Topology 8, no. 4 (October 21, 2008): 1855–959. http://dx.doi.org/10.2140/agt.2008.8.1855.

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24

Spielberg, Jack. "Groupoids and C*-algebras for left cancellative small categories." Indiana University Mathematics Journal 69, no. 5 (2020): 1579–626. http://dx.doi.org/10.1512/iumj.2020.69.7969.

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25

Van Schil, Paul E. "Non-small cell lung cancer: the new T1 categories." F1000Research 6 (February 22, 2017): 174. http://dx.doi.org/10.12688/f1000research.10600.1.

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Recently, major changes have occurred in the staging, diagnosis, and treatment of early stage lung cancer. By screening high-risk populations, we are now able to detect lung cancers at an early stage, but the false-positive rate is high. A new pathological classification was published in 2011 and fully incorporated in the 2015 World Health Organisation (WHO) Classification of Tumours of the Lung, Pleura, Thymus, and Heart. The new eighth edition of the tumour–node–metastasis (TNM) staging system has been fully published and will be in use from January 2017. T1 lesions are subdivided into T1a, T1b, and T1c lesions corresponding to lung cancers up to 10 mm, between 11 and 20 mm, and between 21 and 30 mm, respectively. To determine the size, only the solid part on computed tomographic scanning of the chest and the invasive part on pathological examination will be considered. Prognosis is significantly better for the smallest lesions. For some specific subgroups, sublobar resection may be oncologically valid and yield good long-term outcome, but the results of recently performed randomised trials are awaited.

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26

Dong, Jingcheng, Sonia Natale, and Leandro Vendramin. "Frobenius property for fusion categories of small integral dimension." Journal of Algebra and Its Applications 14, no. 02 (October 19, 2014): 1550011. http://dx.doi.org/10.1142/s0219498815500115.

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Let k be an algebraically closed field of characteristic zero. In this paper, we prove that fusion categories of Frobenius–Perron dimensions 84 and 90 are of Frobenius type. Combining this with previous results in the literature, we obtain that every weakly integral fusion category of Frobenius–Perron dimension less than 120 is of Frobenius type.

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27

Pavlović, Duško. "On completeness and cocompleteness in and around small categories." Annals of Pure and Applied Logic 74, no. 2 (July 1995): 121–52. http://dx.doi.org/10.1016/0168-0072(94)00035-2.

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28

Ilias, Amrani. "Model structure on the category of small topological categories." Journal of Homotopy and Related Structures 10, no. 1 (June 27, 2013): 63–70. http://dx.doi.org/10.1007/s40062-013-0041-8.

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29

Krämer, Thomas, and Rainer Weissauer. "Semisimple super Tannakian categories with a small tensor generator." Pacific Journal of Mathematics 276, no. 1 (July 1, 2015): 229–48. http://dx.doi.org/10.2140/pjm.2015.276.229.

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30

Minian, Elias Gabriel. "Spectra of Small Categories and Infinite Loop Space Machines." K-Theory 37, no. 3 (March 2006): 249–61. http://dx.doi.org/10.1007/s10977-006-0017-0.

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31

Pirashvili, Teimuraz. "On the Center and Baues–Wirsching Cohomology of Small Categories." gmj 16, no. 1 (March 2009): 131–44. http://dx.doi.org/10.1515/gmj.2009.131.

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32

Manovich, Lev. "Can We Think Without Categories?" Digital Culture & Society 4, no. 1 (March 1, 2018): 17–28. http://dx.doi.org/10.14361/dcs-2018-0103.

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Abstract In this article methods developed for the purpose of what I call “Media Analytics” are contextualized, put into a historical framework and discussed in regard to their relevance for “Cultural Analytics”. Largescale analysis of media and interactions enable NGOs, small and big businesses, scientific research and civic media to create insight and information on various cultural phenomena. They provide quantitative analytical data about aspects of digital culture and are instrumental in designing procedural components for digital applications such as search, recommendations, and contextual advertising. A survey on key texts and propositions from 1830 on until the present sketches the development of “Data Society’s Mind”. I propose that even though Cultural Analytics research uses dozens of algorithms, behind them there is a small number of fundamental paradigms. We can think them as types of data society’s and AI society’s cognition. The three most general paradigmatic approaches are data visualization, unsupervised machine learning, and supervised machine learning. I will discuss important challenges for Cultural Analytics research. Now that we have very large cultural data available, and our computers can do complex analysis quite quickly, how shall we look at culture? Do we only use computational methods to provide better answers to questions already established in the 19th and 20th century humanities paradigms, or do these methods allow fundamentally different new concepts?

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33

Raptis, G., and J. Rosický. "Erratum to “Small presentations of model categories and Vopěnka’s principle”." Homology, Homotopy and Applications 23, no. 2 (2021): 375–78. http://dx.doi.org/10.4310/hha.2021.v23.n2.a20.

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34

Seo,Ha-Seok. "The functional categories and their semantic properties of small clauses." Korean Journal of English Language and Linguistics 7, no. 3 (September 2007): 389–410. http://dx.doi.org/10.15738/kjell.7.3.200709.389.

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35

Cegarra, Antonio M. "Cohomology of Homotopy Colimits of Simplicial Sets and Small Categories." Mathematics 8, no. 6 (June 16, 2020): 981. http://dx.doi.org/10.3390/math8060981.

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This paper deals with well-known weak homotopy equivalences that relate homotopy colimits of small categories and simplicial sets. We show that these weak homotopy equivalences have stronger cohomology-preserving properties than for local coefficients.

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36

Moser, Philippe. "Baire categories on small complexity classes and meager–comeager laws." Information and Computation 206, no. 1 (January 2008): 15–33. http://dx.doi.org/10.1016/j.ic.2007.10.002.

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37

Husainov, Ahmet A. "On the homology of small categories and asynchronous transition systems." Homology, Homotopy and Applications 6, no. 1 (2004): 439–71. http://dx.doi.org/10.4310/hha.2004.v6.n1.a22.

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38

Dell’Ambrogio, Ivo. "The unitary symmetric monoidal model category of small C*-categories." Homology, Homotopy and Applications 14, no. 2 (2012): 101–27. http://dx.doi.org/10.4310/hha.2012.v14.n2.a7.

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39

EDIE-MICHELL, CAIN. "THE CLASSIFICATION OF CATEGORIES GENERATED BY AN OBJECT OF SMALL DIMENSION." Bulletin of the Australian Mathematical Society 99, no. 03 (April 11, 2019): 521–22. http://dx.doi.org/10.1017/s0004972719000388.

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40

Bowman, Claudia, Austin Viall, Adam Rudinsky, Chen Gilor, and Jean-Sébastien Palerme. "Hypocholesterolemia in cats: a multicenter retrospective study of 106 cats." Journal of Feline Medicine and Surgery 22, no. 8 (November 11, 2019): 768–73. http://dx.doi.org/10.1177/1098612x19886398.

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Objectives The aim of this study was to describe the clinicopathologic findings and associated diseases found in a population of hypocholesterolemic cats referred to two tertiary care facilities. Methods An electronic medical record search was performed at two veterinary university referral centers to identify cats with serum cholesterol values below the reference interval between January 2004 and 2016. Clinicopathologic data were reviewed for each case and cats were classified into specific disease categories based on clinical diagnosis. Median cholesterol values were compared between disease categories, as well as between survivors and non-survivors. Results In total, 106 hypocholesterolemic cats were included. The median age of the cats was 6 years (range 0.24–18 years). The most common disease categories were gastrointestinal (25.9%), hepatobiliary (19.8%), hematologic (14.8%) and urogenital (14.8%). Though median serum cholesterol values did not differ significantly between survivors and non-survivors, cats with concurrent hypoalbuminemia were at higher risk (odds ratio 15.6, 95% confidence interval 5.2–46.6; P <0.0001) of not surviving to discharge than cats with normal serum albumin concentrations. Conclusions and relevance Taken together, our data suggest that while the degree of hypocholesterolemia did not appear to influence survival rates, the concurrent presence of hypocholesterolemia and hypoalbuminemia was associated with a worse prognosis.

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41

Noble, H. Morgan. "PROBLEMS WITH SMALL CRAFT HARBORS." Coastal Engineering Proceedings 1, no. 6 (January 29, 2011): 38. http://dx.doi.org/10.9753/icce.v6.38.

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Administration of a small craft harbor includes, among its problems, those of finance, law, public relations, policing, and engineering. This paper will relate experiences in all of these categories, but as it is written for Coastal Engineers, it will cover the engineering category most completely.

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42

Straka, Jerry M., and Edward R. Mansell. "A Bulk Microphysics Parameterization with Multiple Ice Precipitation Categories." Journal of Applied Meteorology 44, no. 4 (April 1, 2005): 445–66. http://dx.doi.org/10.1175/jam2211.1.

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Abstract A single-moment bulk microphysics scheme with multiple ice precipitation categories is described. It has 2 liquid hydrometeor categories (cloud droplets and rain) and 10 ice categories that are characterized by habit, size, and density—two ice crystal habits (column and plate), rimed cloud ice, snow (ice crystal aggregates), three categories of graupel with different densities and intercepts, frozen drops, small hail, and large hail. The concept of riming history is implemented for conversions among the graupel and frozen drops categories. The multiple precipitation ice categories allow a range of particle densities and fall velocities for simulating a variety of convective storms with minimal parameter tuning. The scheme is applied to two cases—an idealized continental multicell storm that demonstrates the ice precipitation process, and a small Florida maritime storm in which the warm rain process is important.

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43

Ma, Zizhu. "Generalized Enrichments of Categories for Operads." Algebra Colloquium 14, no. 01 (March 2007): 61–78. http://dx.doi.org/10.1142/s1005386707000077.

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Most enriched categories also have an ordinary category structure which is compatible with the enrichment on them. In this paper, enrichments in a monoidal category are generalized to arbitrary categories. These specialize to the classical enrichments when sets are regraded as discrete categories. We also generalize the definitions of PROs and PROPs as some generalized enrichments of categories. Then an operad in some monoidal category corresponds to a generalized PROP. Algebras of operads induce some special kind of monoidal functors. In the category of small categories, we construct several operads to define lax monoids and lax commutative monoids which are formal descriptions of natural associativity and commutativity. Using this identification, operads and their algebras can be studied by lax commutative monoids and morphisms between them.

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44

KVAMME, SONDRE. "GORENSTEIN PROJECTIVE OBJECTS IN FUNCTOR CATEGORIES." Nagoya Mathematical Journal 240 (December 26, 2018): 1–41. http://dx.doi.org/10.1017/nmj.2018.44.

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Let $k$ be a commutative ring, let ${\mathcal{C}}$ be a small, $k$-linear, Hom-finite, locally bounded category, and let ${\mathcal{B}}$ be a $k$-linear abelian category. We construct a Frobenius exact subcategory ${\mathcal{G}}{\mathcal{P}}({\mathcal{G}}{\mathcal{P}}_{P}({\mathcal{B}}^{{\mathcal{C}}}))$ of the functor category ${\mathcal{B}}^{{\mathcal{C}}}$, and we show that it is a subcategory of the Gorenstein projective objects ${\mathcal{G}}{\mathcal{P}}({\mathcal{B}}^{{\mathcal{C}}})$ in ${\mathcal{B}}^{{\mathcal{C}}}$. Furthermore, we obtain criteria for when ${\mathcal{G}}{\mathcal{P}}({\mathcal{G}}{\mathcal{P}}_{P}({\mathcal{B}}^{{\mathcal{C}}}))={\mathcal{G}}{\mathcal{P}}({\mathcal{B}}^{{\mathcal{C}}})$. We show in examples that this can be used to compute ${\mathcal{G}}{\mathcal{P}}({\mathcal{B}}^{{\mathcal{C}}})$ explicitly.

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45

Kurmashev, Aidar, and Houman Sadri. "UNDERSTANDING CRITERIA FOR DEFINING SMALL AND MIDDLE POWERS." Central Asia's Affairs 88, no. 4 (December 15, 2022): 7–22. http://dx.doi.org/10.52536/2788-5909.2022-4.01.

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International Relations (IR) scholars generally categorize states into three groups of powers: small, middle, or great. The lack of clear criteria for determining the power status of states, however, often creates debate about how to appropriately categorize a particular country. This article focuses on gathering and organizing the major definitions of small and middle powers by various scholars. Moreover, the article places these definitions into different clear and usable categories. Therefore, we illustrate the appropriate range of the small and middle size power categories. This, in turn, will provide clearer guidelines for states that aim to move from one category to another.

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46

Ortega, Eduard, and Enrique Pardo. "The tight groupoid of the inverse semigroups of left cancellative small categories." Transactions of the American Mathematical Society 373, no. 7 (April 29, 2020): 5199–234. http://dx.doi.org/10.1090/tran/8100.

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47

Li, Demei, and Lin Xin. "Lattices Induced by Modular Pull-back Exact Categories." Algebra Colloquium 19, no. 04 (October 15, 2012): 713–26. http://dx.doi.org/10.1142/s1005386712000594.

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In this paper, we introduce the notion of a modular pull-back exact category, study modular lattices [Formula: see text] and [Formula: see text] on the skeletally small modular pull-back exact category (𝒞,ℰ) and show that there is an isomorphism between these two lattices. We also study short exact sequences of lattices induced by ℰ-exact sequences.

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48

Sherman, Clayton. "K1 of Exact Categories by Mirror Image Sequences." Journal of K-Theory 11, no. 1 (April 19, 2012): 155–81. http://dx.doi.org/10.1017/is012003019jkt187.

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AbstractWe establish a presentation for K1 of any small exact category P, based on the notion of “mirror image sequence,” originally introduced by Grayson in 1979; as part of the proof, we show that every element of K1(P) arises from a mirror image sequence. This provides an alternative to Nenashev's presentation in terms of “double short exact sequences.”

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49

Tabuada, Gonçalo. "Homotopy theory of well-generated algebraic triangulated categories." Journal of K-Theory 3, no. 1 (February 11, 2008): 53–75. http://dx.doi.org/10.1017/is007011019jkt021.

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AbstractFor every regular cardinal α, we construct a cofibrantly generated Quillen model structure on a category whose objects are essentially dg categories which are stable under suspensions, cosuspensions, cones and α-small sums.Using results of Porta, we show that the category of well-generated (algebraic) triangulated categories in the sense of Neeman is naturally enhanced by our Quillen model category.

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50

Hansen, Kai Victor. "Food and meals in caring institutions – a small dive into research." International Journal of Health Care Quality Assurance 29, no. 4 (May 9, 2016): 380–406. http://dx.doi.org/10.1108/ijhcqa-08-2015-0092.

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Purpose – With the growing older population, the increasing interest in the elderly’s eating habits and the meal situation go hand in hand and are challenges in many countries, including Norway. The purpose of this paper is to investigate, part of an ongoing project in Norway, address four categories of elderly people: healthy elderly (HE), old people with home care, elderly living in institutions, and critical ill elderly. Design/methodology/approach – The aim of this study was to investigate related articles concerning food and the elderly in the four identified categories, defining six different meal experience categories to disclose possible gaps in the research in terms of core product, room, personal service, company, atmosphere, and management control systems (MCS). Database searches, conducted through JSTOR and Web of Science, started with words in combination with “elderly and meal experiences” and were narrowed down to the most relevant papers with words from the six meal experience categories. Ultimately, 21 of 51 downloaded papers from international journals were reviewed. Findings – A comparison of the four elderly groups was made across the six different meal experience categories, which disclosed several gaps. Among the 21 papers, five focused on HE, 12 on older people living with home care, 16 on elderly living in institutions, and one on critical ill elderly. The specific under-researched gaps include room, company, atmosphere, and MCS. Research limitations/implications – Future research will need to investigate these groups more thoroughly, and the research should concentrate on the HE and critical ill in connection with the six meal experience aspects. Originality/value – The combination of meal experience aspects towards different elderly categories is an original perspective on the aim of the literature review.

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