"Hausdorff distance" via conical cocompletion
Stubbe, Isar
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 51 (2010), p. 51-76 / Harvested from Numdam
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Publié le : 2010-01-01
@article{CTGDC_2010__51_1_51_0,
     author = {Stubbe, Isar},
     title = {"Hausdorff distance" via conical cocompletion},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     volume = {51},
     year = {2010},
     pages = {51-76},
     mrnumber = {2650579},
     zbl = {1260.18009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CTGDC_2010__51_1_51_0}
}

Stubbe, Isar. "Hausdorff distance" via conical cocompletion. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 51 (2010) pp. 51-76. http://gdmltest.u-ga.fr/item/CTGDC_2010__51_1_51_0/

[1] [A. Akhvlediani, M. M. Clementino and W. Tholen, 2009] On the categorical meaning of Hausdorff and Gromov distances I, arxiv:0901.0618v1. | MR 2610438 | Zbl 1226.18013

[2] [J. Bénabou, 1967] Introduction to bicategories, Lecture Notes in Math. 47, pp. 1-77. | MR 220789

[3] [M. H. Albert and G. M. Kelly, 1988] The closure of a class of colimits, J. Pure Appl. Algebra 51, pp. 1-17. | MR 941885 | Zbl 0656.18004

[4] [G.M. Kelly and V. Schmitt, 2005] Notes on enriched categories with colimits of some class, Theory Appl. Categ. 14, pp. 399-423. | MR 2211425 | Zbl 1082.18004

[5] [A. Kock, 1972] Monads for which structures are adjoint to units (Version 1), Aarhus Preprint Series 35.

[6] [A. Kock, 1995] Monads for which structures are adjoint to units, J. Pure Appl. Algebra 104, pp. 41-59. | MR 1359690 | Zbl 0849.18008

[7] [F. W. Lawvere, 1973] Metric spaces, generalized logic, and closed categories, Rend. Sem. Mat. Fis. Milano 43, pp. 135-166. Also in: Reprints in Theory Appl. of Categ. 1, 2002. | MR 352214 | Zbl 0335.18006

[8] [J. Paseka and J. Rosický, 2000] Quantales, pp. 245-262 in: Current research in operational quantum logic, Fund. Theories Phys. 111, Kluwer, Dordrecht. | MR 1907163 | Zbl 0962.06017

[9] [K. I. Rosenthal, 1996] The theory of quantaloids, Pitman Research Notes in Mathematics Series 348, Longman, Harlow. | MR 1427263 | Zbl 0845.18003

[10] [R. Street, 1981] Cauchy characterization of enriched categories Rend. Sem. Mat. Fis. Milano 51, pp. 217-233. Also in: Reprints Theory Appl. Categ. 4, 2004. | MR 708046 | Zbl 0538.18005

[11] [R. Street, 1983] Enriched categories and cohomology, Questiones Math. 6, pp. 265-283. | MR 700252 | Zbl 0523.18007

[12] [R. Street, 1983] Absolute colimits in enriched categories, Cahiers Topologie Géom. Différentielle 24, pp. 377-379. | Numdam | MR 749468 | Zbl 0532.18001

[13] [I. Stubbe, 2005] Categorical structures enriched in a quantaloid: categories, distributors and functors, Theory Appl. Categ. 14, pp. 1-45. | MR 2122823 | Zbl 1079.18005

[14] [I. Stubbe, 2006] Categorical structures enriched in a quantaloid: tensored and cotensored categories, Theory Appl. Categ. 16, pp. 283-306. | MR 2223039 | Zbl 1119.18005

[15] [V. Schmitt, 2006] Flatness, preorders and general metric spaces, to appear in Georgain Math. Journal. See also: arxiv:math/0602463vl.

[16] [V. Zöberlein, 1976] Doctrines on 2-categories, Math. Z. 148, pp. 267-279. | MR 424896 | Zbl 0311.18005

[17] [R. F. C. Walters, 1981] Sheaves and Cauchy-complete categories, Cahiers Topol. Géom. Différ. Catég. 22, pp. 283-286. | Numdam | MR 649076 | Zbl 0495.18009