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Journal articles on the topic 'Category of space'

Author: Grafiati

Published: 28 May 2022

Last updated: 30 July 2025

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1

Felix, Yves, and Jean-Claude Thomas. "Loop Space Homology of Spaces of Small Category." Transactions of the American Mathematical Society 338, no. 2 (1993): 711. http://dx.doi.org/10.2307/2154425.

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2

Félix, Yves, and Jean-Claude Thomas. "Loop space homology of spaces of small category." Transactions of the American Mathematical Society 338, no. 2 (1993): 711–21. http://dx.doi.org/10.1090/s0002-9947-1993-1134757-2.

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3

Proudfoot, Nicholas, and Eric Ramos. "The contraction category of graphs." Representation Theory of the American Mathematical Society 26, no. 23 (2022): 673–97. http://dx.doi.org/10.1090/ert/616.

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We study the category whose objects are graphs of fixed genus and whose morphisms are contractions. We show that the corresponding contravariant module categories are Noetherian and we study two families of modules over these categories. The first takes a graph to a graded piece of the homology of its unordered configuration space and the second takes a graph to an intersection homology group whose dimension is given by a Kazhdan–Lusztig coefficient; in both cases we prove that the module is finitely generated. This allows us to draw conclusions about torsion in the homology groups of graph co

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4

BRIGHTWELL, MARK, and PAUL TURNER. "REPRESENTATIONS OF THE HOMOTOPY SURFACE CATEGORY OF A SIMPLY CONNECTED SPACE." Journal of Knot Theory and Its Ramifications 09, no. 07 (2000): 855–64. http://dx.doi.org/10.1142/s0218216500000487.

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We discuss the homotopy surface category of a space which generalizes the 1+1-dimensional cobordism category of circles and surfaces to the situation where one introduces a background space. We explain how for a simply connected background space, monoidal functors from this category to vector spaces can be interpreted in terms of Frobenius algebras with additional structure.

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5

MENNI, MATÍAS, and ALEX SIMPSON. "Topological and limit-space subcategories of countably-based equilogical spaces." Mathematical Structures in Computer Science 12, no. 6 (2002): 739–70. http://dx.doi.org/10.1017/s0960129502003699.

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There are two main approaches to obtaining ‘topological’ cartesian-closed categories. Under one approach, one restricts to a full subcategory of topological spaces that happens to be cartesian closed – for example, the category of sequential spaces. Under the other, one generalises the notion of space – for example, to Scott's notion of equilogical space. In this paper, we show that the two approaches are equivalent for a large class of objects. We first observe that the category of countably based equilogical spaces has, in a precisely defined sense, a largest full subcategory that can be sim

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Hashem, Khaled A., and Nehad N. Morsi. "FuzzyTL-uniform spaces." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–24. http://dx.doi.org/10.1155/ijmms/2006/25094.

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The main purpose of this paper is to introduce a new structure that is a fuzzyTL-uniform space. We show that our structure generates a fuzzy topological space, precisely, a fuzzyT-locality space. Also, we deduce the concept of level uniformities of a fuzzyTL-uniformity. We connect the category of fuzzyTL-uniform spaces with the category of uniform spaces. We establish a necessary and sufficient condition, under which a fuzzyTL-uniformity is probabilistic pseudometrizable. Finally, we define a functor from the category of fuzzyTL-uniform spaces into the category of fuzzyT-locality spaces and we

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Fadell, E., and S. Husseini. "Category of loop spaces of open subsets in euclidean space." Nonlinear Analysis: Theory, Methods & Applications 17, no. 12 (1991): 1153–61. http://dx.doi.org/10.1016/0362-546x(91)90234-r.

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8

Lutava, Svitlana. "THE CATEGORY “SPACE” IN THE HUMANITIES." Naukovì zapiski Nacìonalʹnogo unìversitetu «Ostrozʹka akademìâ». Serìâ «Fìlologìâ» 1, no. 17(85) (2023): 286–91. http://dx.doi.org/10.25264/2519-2558-2023-17(85)-286-291.

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The paper analyzes the contribution of many linguists to the study of the concept of "space", its properties, and the words, that denotes it, outlines existing scholarly approaches to the space semantics study. As a result of consideration of the achievements of scientists in the study of spatial semantics, differences in their views on issues of terminological, identification and classification nature were revealed. Also, considering the lack of a single approach to the identification and classification of the space nominations characteristics in modern linguistics, the paper carries out the

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Goncharova, K. S., and G. Shelomentsev. "The analysis of space category in economic studies." Moscow University Economics Bulletin, no. 5 (September 19, 2022): 22–41. http://dx.doi.org/10.38050/01300105202252.

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Space is one of the key and controversial (in terms of content) categories in economics. It is assumed that the methodological basis of spatial development concept, and, correspondingly, the very concept of space itself are classical (mercantilism) and neoclassical (price theory) theories. However, until now the understanding of its nature and its role in creating and transforming modern socio-economic relations remains a debatable issue. The key method of analysis in this work is semantic analysis. The Authors attempt, on the one hand, to reveal a retrospective transformation of space concept

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Kurtuluş, Mümin, and L. Beril Toktay. "Category Captainship vs. Retailer Category Management under Limited Retail Shelf Space." Production and Operations Management 20, no. 1 (2011): 47–56. http://dx.doi.org/10.1111/j.1937-5956.2010.01141.x.

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11

Wu, Xiu-Yun. "L-interval spaces and some of their properties." Journal of Intelligent & Fuzzy Systems 40, no. 1 (2021): 13–25. http://dx.doi.org/10.3233/jifs-182525.

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In this paper, notions of L-interval spaces and L-2-arity convex spaces are introduced. It is showed that there is a Galois’s connection between the category of L-convex spaces and the category of L-interval spaces. In particular, the category of L-2-arity convex spaces can be embedded in the category of L-interval spaces as a coreflective subcategory. Further, some properties of L-interval spaces are introduced including L-geometric (resp. L-Peano, L-Pasch and L-sand-glass) property. It is proved that an L-2-arity convex space is an L-JHC convex space iff its segment operator has L-Peano prop

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12

Kurbanov, Kh, and S. Yodgarov. "A functor IS in the Category Compact Hausdorff Spaces." Bulletin of Science and Practice 6, no. 3 (2020): 13–22. http://dx.doi.org/10.33619/2414-2948/52/01.

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We construct a space of normed, homogeneous and max-plus-semiadditive functionals and we give its description. Further we establish that the construction of taking of a space of normed, homogeneous and max-plus-semiadditive functionals, forms a normal functor acting in the category of Hausdorff compact spaces and their continuous maps.

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13

Hejduk, Jacek. "One more difference between measure and category." Tatra Mountains Mathematical Publications 49, no. 1 (2011): 9–15. http://dx.doi.org/10.2478/v10127-011-0020-6.

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ABSTRACT The first part of the paper contains some ideas of the density topologies in the measurable spaces. The second part is devoted to the difference between measure and category for the abstract density space related to the separation axioms

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14

Abel, Mart. "ON THE EQUIVALENCE BETWEEN THE CATEGORIES OF LOCALLY SLICEABLE FIBER SPACES AND SHEAVES OF SETS." Asian-European Journal of Mathematics 03, no. 04 (2010): 521–30. http://dx.doi.org/10.1142/s1793557110000404.

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15

Amal, Nurhikma, Juhanis Juhanis, Muh Adnan Hudain, Yasriuddin Yasriuddin, and Muhammad Rachmat Kasmad. "Analysis of Community Participation And Satisfaction of Sports Open Space In The City of Makassar." COMPETITOR: Jurnal Pendidikan Kepelatihan Olahraga 16, no. 2 (2024): 521. https://doi.org/10.26858/cjpko.v16i2.64151.

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The purpose of the study was to determine the level of participation and community satisfaction with sports open space in Makassar. This type of descriptive research uses a survey analysis research design. The population is all visitors to sports open spaces in CPI, Pakui Sayang Park, Sudiang Gor and Macan Park with the number of samples used, namely 50 people with the sampling technique is a random system. The data analysis technique used is descriptive analysis, and categorization analysis through the SPSS 20.00 program at a significant level of 95% or α 0.05. The results showed that; (1) An

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16

Felix, Yves, Stephen Halperin, and Jean-Claude Thomas. "Loop space homology of spaces of LS category one and two." Mathematische Annalen 287, no. 1 (1990): 377–86. http://dx.doi.org/10.1007/bf01446900.

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17

Nemesh, N. T., and S. M. Shteiner. "METRIC AND TOPOLOGICAL FREEDOM FOR SEQUENTIAL OPERATOR SPACES." Vestnik of Samara University. Natural Science Series 20, no. 10 (2017): 55–67. http://dx.doi.org/10.18287/2541-7525-2014-20-10-55-67.

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In 2002 Anselm Lambert in his PhD thesis [1] introduced the deﬁnition of sequential operator space and managed to establish a considerable amount of analogs of corresponding results in operator space theory. Informally speaking, the category of sequential operator spaces is situated ”between” the categories of normed and operator spaces. This article aims to describe free and cofree objects for diﬀerent versions of sequential operator space homology. First of all, we will show that duality theory in above-mentioned category is in many respects analogous to that in the category of normed spaces

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18

Cheng, Jiaojiao. "The category of space in the genre of essay (based on the essays Of V. M. Peskov)." Litera, no. 12 (December 2020): 159–67. http://dx.doi.org/10.25136/2409-8698.2020.12.34678.

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The subject of this research is the category of space &ndash; one of the intrinsic text categories that implies the meaning of location and spatial relations, and fulfills a plot-composing and semantic function. Essay is a peculiar genre, at the intersection documentary and fiction styles, which is an important factor affecting the analysis of the category of space. Examination of the category of space in essays is one of the relevant trends in linguistics. Essays of the prominent Soviet writer, photographer and journalist V. M. Peskov, which were recognized as the exemplary, serve as the

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19

Khodaii, Somayyeh, Ali Estaji, and Seid Anvariyeh. "On category of T-rough sets." Filomat 36, no. 6 (2022): 1873–93. http://dx.doi.org/10.2298/fil2206873k.

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We introduce three new categories in which their objects are T-approximation spaces and they are denoted by NTAprS, RNTAprS, and LNTAprS. We verify the existence or nonexistence of products and coproducts in these three categories and characterized theirs epimorphisms and monomorphisms. We discuss equalizer and coequalizer of a pair of morphisms in the three categories. We introduce the notion of idempotent approximation space, and we show that idempotent approximation spaces and right upper natural transformations form a category, which is denoted by RNTApr2S. Let CS be the category of all cl

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20

Nikitina, Irina Petrovna. "Artistic Space as a Modern Aesthetical Category." Journal of Flm Arts and Film Studies 5, no. 2 (2013): 66–80. http://dx.doi.org/10.17816/vgik5266-80.

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The article describes the process of transforming the concept of “artistic space” into a category of modern aesthetics due to the work of various 20th century philosophers (O. Spengler, M. Heidegger, P. Florensky, etc.) The author argues that unlike the chronotope, which is a local notion relevant only for temporal arts, the notion of “artistic space” is universal and valid for all art-forms.

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21

Broto, Carles, Ran Levi, and Bob Oliver. "Loop space homology of a small category." Annals of K-Theory 6, no. 3 (2021): 425–80. http://dx.doi.org/10.2140/akt.2021.6.425.

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22

Pavlenko, Yu. "POTENTIAL ENERGY IS A CATEGORY OF SPACE." TRANSBAIKAL STATE UNIVERSITY JOURNAL 28, no. 3 (2022): 14–20. http://dx.doi.org/10.21209/2227-9245-2022-28-3-14-20.

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A theoretical model of potential energy is presented as a world space filled with “dormant” energy waves of low oscillation frequency, diverse in configuration. It has been established that the interaction of locally manifested wave processes of quantum fluctuations, interference and diffraction in areas of increased energy concentration upon reaching the anomalous threshold oscillation frequency of 734 Hz forms elementary particles with a denser mass, increased energy charge and other characteristics characteristic of baryonic matter. The relevance of the research is observed in the expedienc

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23

Мильчакова, Н. Н., and Т. Я. Гончарук. "Space as a category of economic theory." Экономика и предпринимательство, no. 7(120) (July 9, 2020): 110–13. http://dx.doi.org/10.34925/eip.2020.120.7.019.

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Интенсивная разработка и исследование проблем экономической теории в существующем миропорядке ставит все больше вопросов относительно ее понятийного аппарата, структурной трансформации, закономерностей развития. При этом процесс постулирования, уточнения и конкретизации понятий, используемых экономической теорией, определяется ориентацией на возможность эмпирического применения. В связи с этим, существующие предметно-объектные отношения рассматриваются как форма реализации экономических интересов в экономическом пространстве. В статье проведен структурно-институциональный анализ понятия «эконо

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Гончарук, Т. Я., and С. В. Шарамеева. "Space as a category of economic theory." Экономика и предпринимательство, no. 12(125) (February 16, 2021): 568–70. http://dx.doi.org/10.34925/eip.2021.125.12.110.

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Интенсивная разработка и исследование проблем экономической теории в существующем миропорядке ставит все больше вопросов относительно ее понятийного аппарата, структурной трансформации, закономерностей развития. При этом процесс постулирования, уточнения и конкретизации понятий, используемых экономической теорией, определяется ориентацией на возможность эмпирического применения. В связи с этим, существующие предметно-объектные отношения рассматриваются как форма реализации экономических интересов в экономическом пространстве. В статье проведен структурно-институциональный анализ понятия «эконо

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25

Dildora KUVANDIKOVA. "STUDY OF THE “SPACE” CATEGORY IN LINGUISTICS." UzMU xabarlari 1, no. 1.1 (2024): 248–51. http://dx.doi.org/10.69617/uzmu.v1i1.1.466.

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This article provides a comprehensive overview of linguistic research on the category of space, encompassing studies conducted in Russian, English and Uzbek languages. Over the past decades, scholars from various linguistic traditions have delved into the intricate dimensions of spatial semantics, offering insights into both general theoretical frameworks and language-specific manifestations.

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Wu, Xiu-Yun, and Hui-Min Zhang. "L-convex quasi-uniform spaces." Filomat 36, no. 20 (2022): 6867–83. http://dx.doi.org/10.2298/fil2220867w.

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In this paper, L-convex ?*-remotehood system is introduced and some characterizations of both L-convexity and L-convex remotehood system are obtained. Further, ?*-remote mapping is presented and some of its properties are investigated. Based on this, L-convex quasi-uniformity and L-convex quasiuniformity preserving mapping are introduced. It is proved that L-convex quasi-uniform space and Lconvex space are mutually induced. In addition, the category of L-convex spaces and the category of L-convex ?*-remotehood spaces can be embedded into the category of L-convex quasi-uniform spaces.

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27

James, I. M., and J. R. Morris. "Fibrewise category." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 119, no. 1-2 (1991): 177–90. http://dx.doi.org/10.1017/s0308210500028407.

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SynopsisThe purpose of this paper is to introduce a fibrewise generalisation of category, in the sense of Lusternik–Schnirelmann. This reduces to the classical concept when the space is a point. Fibrewise category may be compared with equivariant category, which has been the subject of some recent research [1,7,8]. Many variations on the basic idea of category have been discussed in the literature, for example the concept of category of a map, but since the generalisations to the fibrewise case are fairly routine they are not considered here.

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Wu, Xiu-Yun, Hui-Min Zhang, and Yu-Jie Liu. "L-(resp. concave) down-directed convergence relation spaces and L-(resp. concave) filter convergence spaces." Filomat 37, no. 17 (2023): 5717–34. http://dx.doi.org/10.2298/fil2317717w.

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Convergence structure and relation are useful tools in interpreting many mathematical structures such as topological spaces and convex spaces. The aim of this paper is to study convergence structures in the framework of L-concave spaces by using relations. Specifically, the notion of L-down-directed relations is introduced and some simple examples are presented. Based on this, notions of L-down-directed convergence relation spaces and L-concave down-directed convergence relations are introduced. It is proved that the category of L-concave internal relation spaces can be embedded into the categ

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Rice, Michael D. "Reflexive objects in topological categories." Mathematical Structures in Computer Science 6, no. 4 (1996): 375–86. http://dx.doi.org/10.1017/s0960129500001079.

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This paper presents several basic results about the non-existence of reflexive objects in cartesian closed topological categories of Hausdorff spaces. In particular, we prove that there are no non-trivial countably compact reflexive objects in the category of Hausdorff k-spaces and, more generally, that any non-trivial reflexive Tychonoff space in this category contains a closed discrete subspace corresponding to a numeral system in the sense of Wadsworth. In addition, we establish that a reflexive Tychonoff space in a cartesian-closed topological category cannot contain a non-trivial continuo

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30

Klymenko, Lada, and Solomiya Yuzva. "MODERN CONCEPTUAL FRAMEWORK OF THE COSMIC SPACE CATEGORY." PROBLEMS OF SEMANTICS, PRAGMATICS AND COGNITIVE LINGUISTICS, no. 42 (2022): 60–71. http://dx.doi.org/10.17721/2663-6530.2022.42.07.

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The article is devoted to the cosmic space category and its semantic meaning peculiarities. The interpretation of culture as a horizon of universal, that is, cosmic values, for all hours, was tied to the Cosmos. The national and cultural specificity of the cosmic space category was analyzed and its general characteristics were outlined. Also, the stages of the historical evolution of the studied category were profoundly focused. Given the results of the analysis the paper outlines the historical semantic shift and semantic expansion of this category. The vocabulary representing the concept was

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31

Grady, Ryan, and Owen Gwilliam. "LIE ALGEBROIDS AS SPACES." Journal of the Institute of Mathematics of Jussieu 19, no. 2 (2018): 487–535. http://dx.doi.org/10.1017/s1474748018000075.

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In this paper, we relate Lie algebroids to Costello’s version of derived geometry. For instance, we show that each Lie algebroid – and the natural generalization to dg Lie algebroids – provides an (essentially unique) $L_{\infty }$ space. More precisely, we construct a faithful functor from the category of Lie algebroids to the category of $L_{\infty }$ spaces. Then we show that for each Lie algebroid $L$, there is a fully faithful functor from the category of representations up to homotopy of $L$ to the category of vector bundles over the associated $L_{\infty }$ space. Indeed, this functor s

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32

Kurbanov, Kh., and S. Yodgarov. "10.33619/2414-2948/52/01." Bulletin of Science and Practice 6, no. 3 (2020): 13–22. https://doi.org/10.5281/zenodo.3909704.

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We construct a space of normed, homogeneous, and max-plus-semi-additive functionals and we give its description. Further, we establish that the construction of taking of a space of normed, homogeneous, and max-plus-semi-additive functionals forms normal functor acting in the category of Hausdorff compact spaces and their continuous maps.

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33

Bayaz, Daraby, Delzendeh Fataneh, and Rahimi Asghar. "Parseval's equality in fuzzy normed linear spaces." MATHEMATICA 63 (86), no. 1 (2021): 47–57. http://dx.doi.org/10.24193/mathcluj.2021.1.05.

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We investigate Parseval's equality and define the fuzzy frame on Felbin fuzzy Hilbert spaces. We prove that C(Omega) (the vector space of all continuous functions on Omega) is normable in a Felbin fuzzy Hilbert space and so defining fuzzy frame on C(Omega) is possible. The consequences for the category of fuzzy frames in Felbin fuzzy Hilbert spaces are wider than for the category of the frames in the classical Hilbert spaces.

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34

Wu, Mengchu, Ozgun Caliskan Demirag, Weili Xue, and Minghui Xu. "Retail category management under shelf-space dependent demand: The effectiveness of category captainship." International Journal of Production Economics 276 (October 2024): 109365. http://dx.doi.org/10.1016/j.ijpe.2024.109365.

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Hardie, K. A., K. H. Kamps, and T. Porter. "The coherent homotopy category over a fixed space is a category of fractions." Topology and its Applications 40, no. 3 (1991): 265–74. http://dx.doi.org/10.1016/0166-8641(91)90109-y.

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36

Khare, Mona, and Surabhi Tiwari. "Approach Merotopological Spaces and their Completion." International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–16. http://dx.doi.org/10.1155/2010/409804.

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This paper introduces the concept of an approach merotopological space and studies its category-theoretic properties. Various topological categories are shown to be embedded into the category whose objects are approach merotopological spaces. The order structure of the family of all approach merotopologies on a nonempty set is discussed. Employing the theory of bunches, bunch completion of an approach merotopological space is constructed. The present study is a unified look at the completion of metric spaces, approach spaces, nearness spaces, merotopological spaces, and approach merotopologica

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Smith, Samuel Bruce. "Rational L.S. category of function space components for {$F\sb 0$}-spaces." Bulletin of the Belgian Mathematical Society - Simon Stevin 6, no. 2 (1999): 295–304. http://dx.doi.org/10.36045/bbms/1103141037.

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Ahsanullah, T. M. G., and Gunther Jäger. "Quantale-Valued Uniformizations of Quantale-Valued Generalizations of Approach Groups." New Mathematics and Natural Computation 15, no. 03 (2019): 517–38. http://dx.doi.org/10.1142/s1793005719500303.

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We introduce the categories of quantale-valued approach uniform spaces and quantale-valued uniform gauge spaces, and prove that they are topological categories. We first show that the category of quantale-valued uniform gauge spaces is a full bireflective subcategory of the category of quantale-valued approach uniform spaces and; second, we prove that only under strong restrictions on the quantale these two categories are isomorphic. Besides presenting embeddings of the category of quantale-valued metric spaces into the categories of quantale-valued approach uniform spaces as well as quantale-

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39

Sonck, Gert. "An Ascoli theorem for sequential spaces." International Journal of Mathematics and Mathematical Sciences 26, no. 5 (2001): 303–15. http://dx.doi.org/10.1155/s0161171201004264.

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Ascoli theorems characterize precompact subsets of the set of morphisms between two objects of a category in terms of equicontinuity and pointwise precompactness, with appropriate definitions of precompactness and equicontinuity in the studied category. An Ascoli theorem is presented for sets of continuous functions from a sequential space to a uniform space. In our development we make extensive use of the natural function space structure for sequential spaces induced by continuous convergence and define appropriate concepts of equicontinuity for sequential spaces. We apply our theorem i

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40

Fujioka, Tatsuma. "Transition of Japanese commercial space: What has been lost from the commercial space?" Gremium 3, e1 (2016): 33–42. http://dx.doi.org/10.56039/rgne1a05.

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This paper compares two types commercial spaces in modern Japan, which are shopping mall and “traditional” shopping district called “ShoTenGai”, fromthe viewpoint of commercial space as the third space in the city. Particularly, the ‘’shopping street’’ has been portrayed as nostalgia in the discourse about commercial spaces in Japan. Therefore, the transition of commercial space is always accompanied the description of the “Lost”. However, there is no unanimous opinion in what actually lost in the process of this transition. In this paper, we extract the category of commercial spaces by consid

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Нестеров, А. В. "GENERAL SCIENTIFIC CATEGORY OF INFORMATION SPACE AS A SPACE OF SIGN PRODUCTS." Научно-техническая информация. Серия 1: Организация и методика информационной работы, no. 4 (July 3, 2024): 1–5. http://dx.doi.org/10.36535/0548-0019-2023-04-1.

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Декларируется, что категория информационного пространства характеризует пространство сферы человеческой жизнедеятельности с помощью знак-продуктов в виде знаков, идей и/или форм, отображающих действительное и/или семиотическое содержание отображаемых индивидов. Показана связь сферы информационного пространства со сферами организационного пространства информационных посредников, пространства их информационно-коммуникационных систем, пространства носителей информации, киберпространства, медиапространства и виртуального пространства, а также пространства смарт-систем. It is declared that the cate

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Nesterov, A. V. "General Scientific Category of Information Space as a Space of Sign Products." Scientific and Technical Information Processing 50, no. 2 (2023): 91–95. http://dx.doi.org/10.3103/s014768822302003x.

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Savu, Ionel Dănuț, Bebe Adrian Olei, Sorin Vasile Savu, Gabriel Constantin Benga, and Răzvan Ionuț Iacobici. "Warehousing in Romania." Advanced Engineering Forum 34 (October 2019): 235–40. http://dx.doi.org/10.4028/www.scientific.net/aef.34.235.

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Any perturbation in politics and in economics affects the logistics of freight, from local to regional, national and even international. It creates weaving of the total volume of cargo and subsequently weaving of the market’s necessities regarding the transportation and warehousing. More, weaving of the volume of investments is specific effect. Such mechanism has been recorded in the last 7 years: increasing 2012-2015, decreasing 2015-2017, increasing 2017-2018. From 2017 it has been recorded a higher value of individual transactions, compared to 2016, when the transactions have dropped dramat

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Khosravi, Behnam. "ON FREE AND PROJECTIVE S-SPACES AND FLOWS OVER A TOPOLOGICAL MONOID." Asian-European Journal of Mathematics 03, no. 03 (2010): 443–56. http://dx.doi.org/10.1142/s1793557110000350.

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In this paper, we study free and projective flows and S-spaces, and we characterize free and projective flows over a compact topological monoid S. Similarly, we characterize the same objects in the category of S-spaces for an arbitrary topological monoid S. In fact, we show that any projective S-space is topologically isomorphic to ⊕iϵISei where ei are idempotents in S and ⊕ iϵISei denotes the discrete topological sum of the underlying space of Sei. This is the same result as the category S-Act that the projective objects in this category are the coproducts of Sei's, where ei are idempotents i

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Bunk, Severin, Christian Sämann, and Richard J. Szabo. "The 2-Hilbert space of a prequantum bundle gerbe." Reviews in Mathematical Physics 30, no. 01 (2018): 1850001. http://dx.doi.org/10.1142/s0129055x18500010.

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We construct a prequantum 2-Hilbert space for any line bundle gerbe whose Dixmier–Douady class is torsion. Analogously to usual prequantization, this 2-Hilbert space has the category of sections of the line bundle gerbe as its underlying 2-vector space. These sections are obtained as certain morphism categories in Waldorf’s version of the 2-category of line bundle gerbes. We show that these morphism categories carry a monoidal structure under which they are semisimple and abelian. We introduce a dual functor on the sections, which yields a closed structure on the morphisms between bundle gerbe

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Shaverdo, T. M. "Problematization of the “social space” category in sociology." Proceedings of the National Academy of Sciences of Belarus, Humanitarian Series 67, no. 1 (2022): 21–30. http://dx.doi.org/10.29235/2524-2369-2022-67-1-21-30.

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The article is devoted to the problem of forming a conceptual-categorical apparatus in the field of social topography and reveals the dynamics of problematization of the category “social space” in sociology. The logic of the movement of the research focus in the spatial concepts created by G. Simmel, P. Sorokin and P. Bourdieu are explicated. The ratio of the material and non-material sides of space is analyzed, and the question of the relationship between social structure and spatial forms is considered. With the assistance of R. Carnap and H. Lefebvre’s theoretical schemes are represented tw

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Hanbury, Elizabeth. "An open-closed cobordism category with background space." Algebraic & Geometric Topology 9, no. 2 (2009): 833–63. http://dx.doi.org/10.2140/agt.2009.9.833.

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ZAPATA, CESAR A. IPANAQUE. "CATEGORY AND TOPOLOGICAL COMPLEXITY OF THE CONFIGURATION SPACE." Bulletin of the Australian Mathematical Society 100, no. 3 (2019): 507–17. http://dx.doi.org/10.1017/s0004972719000479.

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The Lusternik–Schnirelmann category cat and topological complexity TC are related homotopy invariants. The topological complexity TC has applications to the robot motion planning problem. We calculate the Lusternik–Schnirelmann category and topological complexity of the ordered configuration space of two distinct points in the product $G\times \mathbb{R}^{n}$ and apply the results to the planar and spatial motion of two rigid bodies in $\mathbb{R}^{2}$ and $\mathbb{R}^{3}$ respectively.

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JERRAM, LEIF. "6. SPACE: A USELESS CATEGORY FOR HISTORICAL ANALYSIS?" History and Theory 52, no. 3 (2013): 400–419. http://dx.doi.org/10.1111/hith.10676.

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del Hoyo, Matias L. "On the loop space of a 2-category." Journal of Pure and Applied Algebra 216, no. 1 (2012): 28–40. http://dx.doi.org/10.1016/j.jpaa.2011.05.001.

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