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Journal articles on the topic 'Topological categories'

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Published: 4 June 2021
Last updated: 10 February 2022

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1

Diers, Yves. "Topological geometrical categories." Journal of Pure and Applied Algebra 168, no. 2-3 (March 2002): 177–87. http://dx.doi.org/10.1016/s0022-4049(01)00095-0.

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2

Shenggang Li. "Weak topological categories." Fuzzy Sets and Systems 93, no. 3 (February 1998): 363–73. http://dx.doi.org/10.1016/s0165-0114(96)00202-3.

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3

Schwarz, Friedhelm. "HEREDITARY TOPOLOGICAL CATEGORIES AND TOPOLOGICAL UNIVERSES." Quaestiones Mathematicae 10, no. 2 (January 1986): 197–216. http://dx.doi.org/10.1080/16073606.1986.9631604.

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4

Tholen, Walter. "Met-Like Categories Amongst Concrete Topological Categories." Applied Categorical Structures 26, no. 5 (February 12, 2018): 1095–111. http://dx.doi.org/10.1007/s10485-018-9513-7.

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5

Ad�mek, J., and G. E. Strecker. "Injectivity of topological categories." Algebra Universalis 26, no. 3 (October 1989): 284–306. http://dx.doi.org/10.1007/bf01211836.

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6

Rice, Michael D. "Reflexive objects in topological categories." Mathematical Structures in Computer Science 6, no. 4 (August 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 continuous image of the unit interval. Therefore, if there exists a non-trivial reflexive Tychonoff space, it does not have a nice geometric structure.
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7

Dikranjan, D., E. Giuli, and A. Tozzi. "TOPOLOGICAL CATEGORIES AND CLOSURE OPERATORS." Quaestiones Mathematicae 11, no. 3 (January 1988): 323–37. http://dx.doi.org/10.1080/16073606.1988.9632148.

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8

Barr, Michael. "Topological $\ast$-autonomous categories, revisited." Tbilisi Mathematical Journal 10, no. 3 (June 2017): 51–64. http://dx.doi.org/10.1515/tmj-2017-0102.

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9

Gurski, Nick, Niles Johnson, and Angelica M. Osorno. "Topological Invariants from Higher Categories." Notices of the American Mathematical Society 66, no. 08 (September 1, 2019): 1. http://dx.doi.org/10.1090/noti1934.

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10

Cagliari, F., and S. Mantovani. "Localizations in universal topological categories." Proceedings of the American Mathematical Society 103, no. 2 (February 1, 1988): 639. http://dx.doi.org/10.1090/s0002-9939-1988-0943097-7.

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11

Solovyov, Sergey A. "On fuzzification of topological categories." Fuzzy Sets and Systems 238 (March 2014): 1–25. http://dx.doi.org/10.1016/j.fss.2013.05.003.

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12

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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13

Shen, Lili, and Walter Tholen. "Topological categories, quantaloids and Isbell adjunctions." Topology and its Applications 200 (March 2016): 212–36. http://dx.doi.org/10.1016/j.topol.2015.12.020.

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14

Baran, Mehmet. "PreT 2 Objects in Topological Categories." Applied Categorical Structures 17, no. 6 (September 11, 2008): 591–602. http://dx.doi.org/10.1007/s10485-008-9161-4.

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15

Baran, M., and H. Altindis. "T 2 -objects in topological categories." Acta Mathematica Hungarica 71, no. 1-2 (1996): 41–48. http://dx.doi.org/10.1007/bf00052193.

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16

Lowen-Colebunders, E., and Z. G. Szabo. "Simplicity of Categories Defined by Symmetry Axioms." Canadian Mathematical Bulletin 34, no. 2 (June 1, 1991): 240–48. http://dx.doi.org/10.4153/cmb-1991-039-0.

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AbstractWe consider two generalizations R0w and R0 of the usual symmetry axiom for topological spaces to arbitrary closure spaces and convergence spaces. It is known that the two properties coincide on Top and define a non-simple subcategory. We show that R0W defines a simple subcategory of closure spaces and R0 a non-simple one. The last negative result follows from the stronger statement that every epireflective subcategory of R0 Conv containing all T1 regular topological spaces is not simple. Similar theorems are shown for the topological categories Fil and Mer.
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17

Kelly, G. M., and F. Rossi. "Topological categories with many symmetric monoidal closed structures." Bulletin of the Australian Mathematical Society 31, no. 1 (February 1985): 41–59. http://dx.doi.org/10.1017/s0004972700002264.

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It would seem from results of Foltz, Lair, and Kelly that symmetric monoidal closed structures, and even monoidal biclosed ones, are quite rare on one-sorted algebraic or essentially-algebraic categories. They showed many such categories to admit no such structures at all, and others to admit only one or two; no such category is known to admit an infinite set of such structures.Among concrete categories, topological ones are in some sense at the other extreme from essentially-algebraic ones; and one is led to ask whether a topological category may admit many such structures. On the category of topological spaces itself, only one such structure - in fact symmetric - is known; although Greve has shown it to admit a proper class of monoidal closed structures. One of our main results is a proof that none of these structures described by Greve, except the classical one, is biclosed.Our other main result is that, nevertheless, there exist topological categories (of quasi-topological spaces) which admit a proper class of symmetric monoidal closed structures. Even if we insist (like most authors) that topological categories must be wellpowered, we can still exhibit ones with more such structures than any small cardinal.
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18

ABEL, MART. "ABOUT SOME CATEGORIES OF SEGAL TOPOLOGICAL ALGEBRAS." Poincare Journal of Analysis and Applications 06, no. 01 (June 29, 2019): 1–14. http://dx.doi.org/10.46753/pjaa.2019.v06i01.001.

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19

Kerkhoff, Sebastian. "Dualizing clones into categories of topological spaces." Algebra universalis 72, no. 4 (November 19, 2014): 299–321. http://dx.doi.org/10.1007/s00012-014-0303-2.

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20

Carqueville, Nils. "Triangle-generation in topological D-brane categories." Journal of High Energy Physics 2008, no. 04 (April 9, 2008): 031. http://dx.doi.org/10.1088/1126-6708/2008/04/031.

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21

Schwede, Stefan. "The p -order of topological triangulated categories." Journal of Topology 6, no. 4 (May 22, 2013): 868–914. http://dx.doi.org/10.1112/jtopol/jtt018.

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22

Brown, Michael K., and Tobias Dyckerhoff. "Topological $K$-theory of equivariant singularity categories." Homology, Homotopy and Applications 22, no. 2 (2020): 1–29. http://dx.doi.org/10.4310/hha.2020.v22.n2.a1.

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23

Knight, R. W. "Categories of Topological Spaces and Scattered Theories." Notre Dame Journal of Formal Logic 48, no. 1 (January 2007): 53–77. http://dx.doi.org/10.1305/ndjfl/1172787545.

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24

Chigogidze, Alex, and Alexandr Karasev. "Topological Model Categories Generated by Finite Complexes." Monatshefte f�r Mathematik 139, no. 2 (May 1, 2003): 129–50. http://dx.doi.org/10.1007/s00605-002-0532-x.

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25

Banerjee, Abhishek. "A topological nullstellensatz for tensor-triangulated categories." Comptes Rendus Mathematique 356, no. 4 (April 2018): 365–75. http://dx.doi.org/10.1016/j.crma.2018.02.012.

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26

Zarichnyi, M. M., and V. V. Fedorchuk. "Covariant functors in categories of topological spaces." Journal of Soviet Mathematics 53, no. 2 (January 1991): 147–76. http://dx.doi.org/10.1007/bf01098256.

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27

Fedorchuk, V. V. "Functors of probability measures in topological categories." Journal of Mathematical Sciences 91, no. 4 (September 1998): 3157–204. http://dx.doi.org/10.1007/bf02432852.

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28

Činčura, Juraj. "Closed structures on categories of topological spaces." Topology and its Applications 20, no. 2 (August 1985): 179–89. http://dx.doi.org/10.1016/0166-8641(85)90078-1.

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29

Herrlich, Horst. "Topological improvements of categories of structured sets." Topology and its Applications 27, no. 2 (November 1987): 145–55. http://dx.doi.org/10.1016/0166-8641(87)90101-5.

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30

Zhang, Dexue. "Galois connections between categories of -topological spaces." Fuzzy Sets and Systems 152, no. 2 (June 2005): 385–94. http://dx.doi.org/10.1016/j.fss.2004.09.002.

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31

Seal, Gavin J. "Cartesian Closed Topological Categories and Tensor Products." Applied Categorical Structures 13, no. 1 (January 2005): 37–47. http://dx.doi.org/10.1007/s10485-004-2940-7.

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32

Seal, Gavin J. "Free Modules over Cartesian Closed Topological Categories." Applied Categorical Structures 13, no. 2 (April 2005): 181–87. http://dx.doi.org/10.1007/s10485-004-5314-2.

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33

Brochier, Adrien, David Jordan, and Noah Snyder. "On dualizability of braided tensor categories." Compositio Mathematica 157, no. 3 (March 2021): 435–83. http://dx.doi.org/10.1112/s0010437x20007630.

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We study the question of dualizability in higher Morita categories of locally presentable tensor categories and braided tensor categories. Our main results are that the 3-category of rigid tensor categories with enough compact projectives is 2-dualizable, that the 4-category of rigid braided tensor categories with enough compact projectives is 3-dualizable, and that (in characteristic zero) the 4-category of braided multi-fusion categories is 4-dualizable. Via the cobordism hypothesis, this produces respectively two-, three- and four-dimensional framed local topological field theories. In particular, we produce a framed three-dimensional local topological field theory attached to the category of representations of a quantum group at any value of $q$.
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34

AWODEY, STEVEN. "Topological representation of the λ-calculus." Mathematical Structures in Computer Science 10, no. 1 (February 2000): 81–96. http://dx.doi.org/10.1017/s0960129599002972.

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The λ-calculus can be represented topologically by assigning certain spaces to the types and certain continuous maps to the terms. Using a recent result from category theory, the usual calculus of λ-conversion is shown to be deductively complete with respect to such topological semantics. It is also shown to be functionally complete, in the sense that there is always a ‘minimal’ topological model in which every continuous function is λ-definable. These results subsume earlier ones using cartesian closed categories, as well as those employing so-called Henkin and Kripke λ-models.
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35

Dyckerhoff, Tobias. "-homotopy invariants of topological Fukaya categories of surfaces." Compositio Mathematica 153, no. 8 (June 9, 2017): 1673–705. http://dx.doi.org/10.1112/s0010437x17007205.

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We provide an explicit formula for localizing$\mathbb{A}^{1}$-homotopy invariants of topological Fukaya categories of marked surfaces. Following a proposal of Kontsevich, this differential$\mathbb{Z}$-graded category is defined as global sections of a constructible cosheaf of dg categories on any spine of the surface. Our theorem utilizes this sheaf-theoretic description to reduce the calculation of invariants to the local case when the surface is a boundary-marked disk. At the heart of the proof lies a theory of localization for topological Fukaya categories which is a combinatorial analog of Thomason–Trobaugh’s theory of localization in the context of algebraic$K$-theory for schemes.
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36

Pestov, Vladimir G. "Universal arrows to forgetful functors from categories of topological algebra." Bulletin of the Australian Mathematical Society 48, no. 2 (October 1993): 209–49. http://dx.doi.org/10.1017/s0004972700015665.

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We survey the present trends in theory of universal arrows to forgetful functors from various categories of topological algebra and functional analysis to categories of topology and topological algebra. Among them are free topological groups, free locally convex spaces, free Banach-Lie algebras, and more. An accent is put on the relationship of those constructions with other areas of mathematics and their possible applications. A number of open problems is discussed; some of them belong to universal arrow theory, and other may become amenable to the methods of this theory.
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37

Weck-Schwarz, Sibylle. "To-OBJECTS AND SEPARATED OBJECTS IN TOPOLOGICAL CATEGORIES." Quaestiones Mathematicae 14, no. 3 (July 1991): 315–25. http://dx.doi.org/10.1080/16073606.1991.9631649.

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38

Duplij, Steven, and Wladyslaw Marcinek. "Regular obstructed categories and topological quantum field theory." Journal of Mathematical Physics 43, no. 6 (June 2002): 3329–41. http://dx.doi.org/10.1063/1.1473681.

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39

Costello, Kevin. "Topological conformal field theories and Calabi–Yau categories." Advances in Mathematics 210, no. 1 (March 2007): 165–214. http://dx.doi.org/10.1016/j.aim.2006.06.004.

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40

Richter, Günther. "Separation properties in algebraic categories of topological spaces." Topology and its Applications 20, no. 1 (July 1985): 79–87. http://dx.doi.org/10.1016/0166-8641(85)90037-9.

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41

Frascella, A., and C. Guido. "Structured lattices and topological categories of L-sets." Fuzzy Sets and Systems 161, no. 3 (February 2010): 444–52. http://dx.doi.org/10.1016/j.fss.2009.09.009.

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42

Alderton, Ian W., and Gabriele Castellini. "Epimorphisms in categories of separated fuzzy topological spaces." Fuzzy Sets and Systems 56, no. 3 (June 1993): 323–30. http://dx.doi.org/10.1016/0165-0114(93)90213-2.

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43

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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44

Činčura, Juraj. "Hereditary Coreflective Subcategories of Categories of Topological Spaces." Applied Categorical Structures 13, no. 4 (August 2005): 329–42. http://dx.doi.org/10.1007/s10485-005-8848-z.

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45

Stine, Jay. "Clopen objects, connected objects, and normalized topological categories." Topology and its Applications 290 (March 2021): 107593. http://dx.doi.org/10.1016/j.topol.2021.107593.

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46

Heath, Philip R., and M. M. Parmenter. "Lifting colimits in various categories." Mathematical Proceedings of the Cambridge Philosophical Society 104, no. 2 (September 1988): 193–97. http://dx.doi.org/10.1017/s0305004100065373.

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In a recent publication [2], R. Brown and the first author proved a Lifting Theorem for groups (and topological groups) showing that if β: B → H is an epimorphism of groups and H is a certain type of colimit of groups, then this colimit can be lifted (or pulled back) through β; that is B is a colimit of the lifted diagram (see Corollary 2·3 below).
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47

VICKERS, STEVEN. "Topical categories of domains." Mathematical Structures in Computer Science 9, no. 5 (October 1999): 569–616. http://dx.doi.org/10.1017/s0960129599002741.

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This paper shows how it is possible to express many techniques of categorical domain theory in the general context of topical categories (where ‘topical’ means internal in the category Top of Grothendieck toposes with geometric morphisms). The underlying topos machinery is hidden by using a geometric form of constructive mathematics, which enables toposes as ‘generalized topological spaces’ to be treated in a transparently spatial way, and also shows the constructivity of the arguments. The theory of strongly algebraic (SFP) domains is given as a case study in which the topical category is Cartesian closed.
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48

ALB, ALINA, and MIHAIL URSUL. "A FEW HOMOLOGICAL CHARACTERIZATIONS OF COMPACT SEMISIMPLE RINGS." Journal of Algebra and Its Applications 04, no. 05 (October 2005): 539–49. http://dx.doi.org/10.1142/s0219498805001411.

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Fix any compact ring R with identity. We associate to R the following categories of topological R-modules: (i) R𝔇 (𝔇R) the category of all discrete topological left (right) R-modules; (ii) Rℭ (ℭR) the category of all compact left (right) R-modules. We have introduced the following notions (analogous with classical notions of module theory): (i) the tensor product [Formula: see text] of A ∈ ℭR and B ∈Rℭ ([Formula: see text] has a structure of a compact Abelian group); (ii) a topologically semisimple module; (iii) a compact topologically flat module. We give a characterization of compact semisimple rings by using of flat modules.
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49

Bello, Hugo J. "The Ext group in the categories of topological abelian groups and topological vector spaces." Topology and its Applications 221 (April 2017): 379–92. http://dx.doi.org/10.1016/j.topol.2017.02.022.

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50

Gevorgyan, P. S., and I. Pop. "Uniformly Movable Categories and Uniform Movability of Topological Spaces." Bulletin of the Polish Academy of Sciences Mathematics 55, no. 3 (2007): 229–42. http://dx.doi.org/10.4064/ba55-3-5.

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