Homotopic pullbacks, Lax pullbacks, and exponentiability
Niefield, Susan
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 47 (2006), p. 50-80 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 2006-01-01
@article{CTGDC_2006__47_1_50_0,
     author = {Niefield, Susan B.},
     title = {Homotopic pullbacks, Lax pullbacks, and exponentiability},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     volume = {47},
     year = {2006},
     pages = {50-80},
     mrnumber = {2220061},
     zbl = {1095.18001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CTGDC_2006__47_1_50_0}
}

Niefield, Susan. Homotopic pullbacks, Lax pullbacks, and exponentiability. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 47 (2006) pp. 50-80. http://gdmltest.u-ga.fr/item/CTGDC_2006__47_1_50_0/

[1] P.S. Alexandrov, Über die Metrisation der im kleinen kompakten topologische Räume, Math. Ann. 92 (1924), 294-301. | JFM 50.0128.04 | MR 1512216

[2] H.J. Baues, Algebraic Homotopy, Cambridge University Press, 1989. | MR 985099 | Zbl 0688.55001

[3] L. Bombelli, J. Lee, D. Meyer, and R. Sorkin, Space-time as a causal set. Phys. Rev. Lett. 59 (1987), 521-524. | MR 899046

[4] F. Conduché, Au sujet de l'existence d'adjoints à droite aux foncteurs "image réciproque" dans la catégorie des catégories, C. R. Acad. Sci. Paris 275 (1972), A891-894. | MR 310033 | Zbl 0242.18012

[5] J. Giraud, Méthode de la descente, Bull. Math. Soc. France, Memoire 2(1964). | Numdam | MR 190142 | Zbl 0211.32902

[6] A. Grothendieck and J.L. Verdier, Theorie des Topos (SGA 4), Springer Lecture Notes in Math. 269-270 (1972), 1-340. | MR 354653 | Zbl 0256.18008

[7] A. Grothendieck, Esquisse d'un programme, London Math. Soc. Lecture Note Ser. 242 (1997), 5-48. | MR 1483107 | Zbl 0901.14001

[8] K. A Hardie, K. H. Kamps, and T. Porter, The coherent homotopy category over a fixed space is a category of fractions, Topology Appl. 40 (1991), 265-274. | MR 1124841 | Zbl 0751.55010

[9] J.M.E. Hyland, Function spaces in the category of locales, Springer Lecture Notes in Math. 871 (1981), 264-281. | Zbl 0483.54005

[10] J.R. Isbell, Atomless parts of spaces, Math. Scand. 31 (1972), 5-32. | MR 358725 | Zbl 0246.54028

[11] P.T. Johnstone, Topos Theory, Academic Press, 1977. | MR 470019 | Zbl 0368.18001

[12] P.T. Johnstone, Stone Spaces, Cambridge University Press, 1982. | MR 698074 | Zbl 0499.54001

[13] P.T. Johnstone and A. Joyal, Continuous categories and exponentiable toposes, J. Pure Appl. Algebra 25 (1982), 255-296. | MR 666021 | Zbl 0487.18003

[14] K.H. Kamps and T. Porter, Abstract homotopy and simple homotopy theory, World Scientific Publishing Co., Inc., River Edge, NJ, 1997. | MR 1464944 | Zbl 0890.55014

[15] R.W. Kieboom, Notes on homotopy pull-backs, Quaest. Math. 14 (1991), 445-452. | MR 1143048 | Zbl 0747.55009

[16] M. Mather, Pull-backs in homotopy, Can. J. Math. 28 (1976), 225-263. | MR 402694 | Zbl 0351.55005

[17] I. Moerdijk and J.J.C. Vermeulen, Proper maps of toposes, Amer. Math. Soc. Memoirs 705 (2000). | MR 1787303 | Zbl 0961.18003

[18] S.B. Niefield, Cartesianness, Ph.D. Thesis, Rutgers University, 1978.

[19] S.B. Niefield, Cartesianness: topological spaces, uniform spaces, and affine schemes, J. Pure Appl. Algebra 23 (1982), 147-167. | MR 639571 | Zbl 0475.18011

[20] S.B. Niefield, Cartesian inclusions: locales and toposes, Comm. in Alg. 9(16) (1981), 1639-1671. | MR 630579 | Zbl 0497.18009

[21] S.B. Niefield, Cartesian spaces over T and locales over Ω(T), Cah. Topol. Géom. Différ. Catég. 23-3 (1982), 257-267. | Numdam | Zbl 0492.18005

[22] S.B. Niefield, Exponentiable morphisms: posets, spaces, locales, and Grothendieck toposes, Theory Appl. Categ. 8 (2001), 16-32. | MR 1815044 | Zbl 1010.06010

[23] S.B. Niefield, Locally compact path spaces, Appl. Categ. Structures 13 (2005), 65-69. | MR 2132744 | Zbl 1076.54014

[24] D.P. Rideout and R.D. Sorkin, Evidence for a continuum limit in causal set dynamics, Phys. Rev. D 63 (2001), 104011. | MR 1840683

[25] D.S. Scott, Continuous lattices, Springer Lecture Notes in Math. 274 (1972), 97-137. | MR 404073 | Zbl 0239.54006