Symmetric monoidal closed structures in 𝑃𝑅𝐴𝑃
Sioen, M.
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 42 (2001), p. 285-316 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 2001-01-01
@article{CTGDC_2001__42_4_285_0,
     author = {Sioen, M.},
     title = {Symmetric monoidal closed structures in $\mathit {PRAP}$},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     volume = {42},
     year = {2001},
     pages = {285-316},
     mrnumber = {1876868},
     zbl = {1004.18008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CTGDC_2001__42_4_285_0}
}

Sioen, M. Symmetric monoidal closed structures in $\mathit {PRAP}$. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 42 (2001) pp. 285-316. http://gdmltest.u-ga.fr/item/CTGDC_2001__42_4_285_0/

[1] Adámek, J. Herrlich, H. and Strecker, G. Abstract and Concrete Categories, John Wiley, New York (1990) | MR 1051419 | Zbl 0695.18001

[2] Banaschewski, B. and Nelson, E. Tensorproducts and Bimorphisms, Canad. Math. Bull., 19(4) (1976), pp. 385-402 | MR 442059 | Zbl 0392.18003

[3] Borceux, F. Handbook of Categorical Algebra I, II, III, Encyclopedia of Mathematics Vol. 50, 51, 52, Cambridge University Press (1994) | Zbl 0911.18001

[4] Brock, P. and Kent, D. C. Approach Spaces, Limit Tower Spaces and Probabilistic Metric Spaces, Appl. Categ. Struct., 5 (1997), pp. 99-110 | MR 1456517 | Zbl 0885.54008

[5] Činčura, J. On a Tensorproduct in Initially Structured Categories, Math. Slovaca, 29(3) (1979), pp. 245-255 | MR 561624 | Zbl 0419.18001

[6] Eilenberg, S. and Kelley, G.M. Closed Categories, Proc. Conf. on Categorical Algebra, La Jolla 1965, Springer Verlag, New-York (1966), pp. 421-562 | MR 225841 | Zbl 0192.10604

[7] Herrlich, H. and Lowen, R. On Simultaneously Reflective and Coreflective Sub-constructs, to appear in G.C.L. Brümmer Festschrift | Zbl 0986.18005

[8] Kannan, V. Reflexive cum Coreflexive Subcategories in Topology, Math. Ann., 195 (1972), pp. 168-174 | MR 291048 | Zbl 0215.09701

[9] Logar, A. and Rossi, F. Monoidal Closed Structures on Categories with Constant Maps, J. Australian Math. Soc. (Ser. A), 38 (1985), pp. 175-185 | MR 770124 | Zbl 0584.18004

[10] Lowen, E. and Lowen, R. Characterization of Convergence in Fuzzy Topological Spaces, Internat. J. Math. Math. Sci., 8(3) (1985), pp. 497-511 | MR 809071 | Zbl 0593.54005

[11] Lowen, E. and Lowen, R. A Quasi-topos Containing CONV and MET as Full Subcategories, Int. J. Math. Math. Sci., 11 (1988), pp. 417-438 | MR 947271 | Zbl 0672.54003

[12] Lowen, E. and Lowen, R. Topological Quasitopos Hulls of Categories Containing Topological and Metric Objects, Cah. Top. Géom. Diff. Catég., 30 (1989), pp. 213-238 | Numdam | MR 1029625 | Zbl 0706.18002

[13] Lowen, E., Lowen, R. and Verbeeck, C. Exponential Objects in the Construct PRAP, Cah. Top. Géom. Diff. Catég., XXXVIII(4) (1997), pp. 259-276 | Numdam | MR 1487961 | Zbl 0888.54015

[14] Lowen-Colebunders, E. and Sonck, G. Exponential Objects and Cartesian Closedness in the Construct PRTOP, Appl. Categ. Struct., 1 (1993), pp. 345-360 | MR 1268508 | Zbl 0796.54019

[15] Lowen, R. Convergence in fuzzy topological spaces, Gen. Top. Appl., 10 (1979), pp. 147-166. | MR 527841 | Zbl 0409.54008

[16] Lowen, R. Approach Spaces: a Common Supercategory of TOP and MET, Math. Nachr. 141 (1989), pp. 183-226 | MR 1014427 | Zbl 0676.54012

[17] Lowen, R. Approach Spaces: the Missing Link in the Topology-Uniformity-Metric Triad, Oxford Mathematical Monographs, Oxford University Press (1997) | MR 1472024 | Zbl 0891.54001

[18] Lowen, R., Vaughan, D. and Verbeeck, C. Convergence Using Generalizations of Filters, to appear

[19] Maclane, S. Natural Associativity and Commutativity, Rice Univ. Studies, 49 (1963), pp. 28-46 | MR 170925 | Zbl 0244.18008

[20] Maclane, S. Categories for the Working Mathematician, Graduate Texts in Mathematics, Springer Verlag, New-York (1971) | MR 354798 | Zbl 0705.18001

[21] Nel, L.D. Initially Structured Categories and Cartesian Closedness, Canad. J. Math., 27 (1975), 1361-1377 | MR 393183 | Zbl 0294.18002

[22] Pumplün, D. Das Tensorprodukt als Universelles Problem, Math. Ann., 171 (1967), pp. 247-262 | MR 212067 | Zbl 0189.01706

[23] Wischnewsky, M.B. Aspects of Categorical Algebra in Initialstructure Categories, Cah. Top. Géom. Diff., XV (1974), pp. 419-444 | Numdam | MR 382389 | Zbl 0324.18002