Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-15T15:37:27.062Z Has data issue: false hasContentIssue false

Bibliography

Published online by Cambridge University Press:  05 June 2014

Emily Riehl
Emily Riehl
Affiliation:
Harvard University, Massachusetts
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Categorical Homotopy Theory , pp. 337 - 342
Publisher: Cambridge University Press
Print publication year: 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] T., Athorne. The coalgebraic structure of cell complexes. Theory Appl. Categ., 26(11):304–330, 2012.Google Scholar
[2] T., Barthel, J. P., May, and E., Riehl. Six model structures for dg-modules over dgas: Model category theory in homological action. Preprint, arXiv:1310.1159 [math.CT], 2013.Google Scholar
[3] T., Barthel and E., Riehl. On the construction of functorial factorizations for model categories. Algebr. Geom. Topol., 13(2):1089–1124, 2013.Google Scholar
[4] T., Beke. Sheafifiable homotopy model categories. Math. Proc. Cambridge Philos. Soc., 129(3):447–475, 2000.Google Scholar
[5] C., Berger and I., Moerdijk. On an extension of the notion of Reedy category. Math. Z., 269(3-4):977-1004, 2011.Google Scholar
[6] J. E., Bergner. A model category structure on the category of simplicial categories. Trans. Amer. Math. Soc., 359(5):2043–2058, 2007.Google Scholar
[7] A. J., Blumberg and E., Riehl. Homotopical resolutions associated to deformable adjunctions. Preprint, arXiv:1208.2844 [math.AT], 2012.Google Scholar
[8] J. M., Boardman and R. M., Vogt. Homotopy invariant algebraic structures on topological spaces. Lecture Notes in Mathematics, Vol. 347. Springer, Berlin, 1973.Google Scholar
[9] F., Borceux. Handbook of categorical algebra. 2. Encyclopedia of Mathematics and Its Applications, vol. 51. Cambridge University Press, Cambridge, 1994.Google Scholar
[10] A. K., Bousfield and D. M., Kan. Homotopy limits, completions and localizations. Lecture Notes in Mathematics, Vol. 304. Springer, Berlin, 1972.Google Scholar
[11] M. C., Bunge. Relative functor categories and categories of algebras. J. Algebra, 11:64-101, 1969.Google Scholar
[12] J. D., Christensen and M., Hovey. Quillen model structures for relative homological algebra. Math. Proc. Cambridge Philos. Soc., 133(2):261–293, 2002.Google Scholar
[13] M., Cole. Mixing model structures. Topology Appl., 153(7):1016–1032, 2006.Google Scholar
[14] J.-M., Cordier and T., Porter. Maps between homotopy coherent diagrams. Topology Appl., 28(3):255–275, 1988.Google Scholar
[15] G. S. H., Cruttwell. Normed spaces and the change of base for enriched categories. PhD thesis, Dalhousie University, 2008.Google Scholar
[16] E. J., Dubuc. Kan extensions in enriched category theory. Lecture Notes in Mathematics, Vol. 145. Springer, Berlin, 1970.Google Scholar
[17] D., Dugger. Replacing model categories with simplicial ones. Trans. Amer. Math. Soc., 353(12):5003–5027, 2001.Google Scholar
[18] D., Dugger. A primer on homotopy colimits. Preprint in progress, available from http://pages.uoregon.edu/ddugger/, 2008.Google Scholar
[19] D., Dugger and D. C., Isaksen. Topological hypercovers and A1 -realizations. Math. Z., 246(4):667–689, 2004.Google Scholar
[20] D., Dugger and D. I., Spivak. Mapping spaces in quasi-categories. Algebr. Geom. Topol., 11(1):263–325, 2011.Google Scholar
[21] D., Dugger and D. I., Spivak. Rigidification of quasi-categories. Algebr. Geom. Topol., 11(1):225–261, 2011.
[22] W. G., Dwyer, P. S., Hirschhorn, D. M., Kan, and J. H., Smith. Homotopy limit functors on model categories and homotopical categories. Mathematical Surveys and Monographs, vol. 113. American Mathematical Society, Providence, RI, 2004.Google Scholar
[23] W. G., Dwyer and D. M., Kan. A classification theorem for diagrams of simplicial sets. Topology, 23(2):139–155, 1984.Google Scholar
[24] W. G., Dwyer and J., Spaliński. Homotopy theories and model categories. In Handbook of algebraic topology, pages 73-126. North-Holland, Amsterdam, 1995.Google Scholar
[25] A. D., Elmendorf, I., Kříž, M. A., Mandell, and J. P., May. Modern foundations for stable homotopy theory. In Handbook of algebraic topology, pages 213-253. North-Holland, Amsterdam, 1995.Google Scholar
[26] T. M., Fiore and W., Lück. Waldhausen additivity: Classical and quasicategorical. Preprint, arXiv:1207.6613. [math.AT], 2012.Google Scholar
[27] R., Fritsch and R. A., Piccinini. Cellular structures in topology. Cambridge Studies in Advanced Mathematics, vol. 19. Cambridge University Press, Cambridge, 1990.Google Scholar
[28] P., Gabriel and M., Zisman. Calculus of fractions and homotopy theory. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 35. Springer, New York, 1967.Google Scholar
[29] N., Gambino. Weighted limits in simplicial homotopy theory. J. Pure Appl. Algebra, 214(7):1193–1199, 2010.Google Scholar
[30] R., Garner. Cofibrantly generated natural weak factorisation systems. Preprint, arXiv:math/0702290. [math.CT], 2007.Google Scholar
[31] R., Garner. Understanding the small object argument. Appl. Categ. Structures, 17(3):247–285, 2009.Google Scholar
[32] P. G., Goerss and J. F., Jardine. Simplicial homotopy theory. Progress in Mathematics, vol. 174. Birkhäuser, Basel, 1999.
[33] M., Grandis and W., Tholen. Natural weak factorization systems. Arch. Math. (Brno), 42(4):397-408, 2006.Google Scholar
[34] B., Gray. Homotopy theory. Pure and Applied Mathematics, Vol. 64. Academic Press, New York, 1975.Google Scholar
[35] A., Hatcher. Algebraic topology. Cambridge University Press, Cambridge, 2002.Google Scholar
[36] P. S., Hirschhorn. Model categories and their localizations. Mathematical Surveys and Monographs, vol. 99. American Mathematical Society, Providence, RI, 2003.Google Scholar
[37] J., Hollender and R. M., Vogt. Modules of topological spaces, applications to homotopy limits and E∞ structures. Arch. Math. (Basel), 59(2):115–129, 1992.Google Scholar
[38] M., Hovey. Model categories. Mathematical Surveys and Monographs, vol. 63. American Mathematical Society, Providence, RI, 1999.Google Scholar
[39] M., Hovey, B., Shipley, and J., Smith. Symmetric spectra. J. Amer. Math. Soc., 13(1):149–208, 2000.Google Scholar
[40] A., Joyal. Quasi-categories and Kan complexes. J. Pure Appl. Algebra, 175(1-3):207-222, 2002. Special volume celebrating the 70th birthday of Professor Max Kelly.Google Scholar
[41] A., Joyal. The theory of quasi-categories and its applications. Preprint in progress, 2008.Google Scholar
[42] A., Joyal. The theory of quasi-categories I. Preprint in progress, 2008.Google Scholar
[43] A., Joyal and M., Tierney. Quasi-categories vs Segal spaces. In Categories in algebra, geometry and mathematical physics. Contemp. Math., vol. 431, pages 277-326. American Mathematical Society, Providence, RI, 2007.Google Scholar
[44] G. M., Kelly. Doctrinal adjunction. In Category Seminar (Proc. Sem., Sydney, 1972/1973). Lecture Notes in Mathematics, Vol. 420, pages 257-280. Springer, Berlin, 1974.Google Scholar
[45] G. M., Kelly. A unified treatment of transfinite constructions for free algebras, free monoids, colimits, associated sheaves, and so on. Bull. Austral. Math. Soc., 22(1):1–83, 1980.Google Scholar
[46] G. M., Kelly. Basic concepts of enriched category theory. Reprints in Theory and Applications of Categories. Reprint of the 1982 original by Cambridge University Press, Cambridge.
[47] G. M., Kelly and R., Street. Review of the elements of 2-categories. In Category Seminar(Proc. Sem., Sydney, 1972/1973). Lecture Notes in Mathematics, Vol.420, pages 75-103. Springer, Berlin, 1974.Google Scholar
[48] S., Lack. Homotopy-theoretic aspects of 2-monads. J. Homotopy Relat. Struct., 2(2):229–260, 2007.Google Scholar
[49] J., Lurie. Higher topos theory. Annals of Mathematics Studies, vol. 170. Princeton University Press, Princeton, NJ, 2009.Google Scholar
[50] S., Mac Lane. Categories for the working mathematician, 2nd ed. Graduate Texts in Mathematics, vol. 5. Springer, New York, 1998Google Scholar
[51] P. J., Malraison Jr.Fibrations as triple algebras. J. Pure Appl. Algebra, 3:287-293, 1973.Google Scholar
[52] G., Maltsiniotis. Le théorème de Quillen, d'adjonction des foncteurs dérivés, revisité. C. R. Math. Acad. Sci. Paris, 344(9):549–552, 2007.Google Scholar
[53] M. A., Mandell and J. P., May. Equivariant orthogonal spectra and S-modules. Mem. Amer. Math. Soc., 159(755):x+108, 2002.Google Scholar
[54] M. A., Mandell, J. P., May, S., Schwede, and B., Shipley. Model categories of diagram spectra. Proc. London Math. Soc., 82(2):441–512, 2001.Google Scholar
[55] J. P., May. Simplicial objects in algebraic topology. Chicago Lectures in Mathematics. Reprint of the 1967 original by University of Chicago Press, Chicago, IL.
[56] J. P., May. Classifying spaces and fibrations. Mem. Amer. Math. Soc., 1(1, 155):xiii+98, 1975.Google Scholar
[57] J. P., May. A concise course in algebraic topology. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 1999.Google Scholar
[58] J. P., May and K., Ponto. More concise algebraic topology: Localization, completion, and model categories. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 2012.Google Scholar
[59] J. P., May and J., Sigurdsson. Parametrized homotopy theory. Mathematical Surveys and Monographs, vol. 132. American Mathematical Society, Providence, RI, 2006.Google Scholar
[60] M. C., McCord. Classifying spaces and infinite symmetric products. Trans. Amer. Math. Soc., 146:273-298, 1969.Google Scholar
[61] D., McDuff. On the classifying spaces of discrete monoids. Topology, 18(4):313–320, 1979.Google Scholar
[62] J.-P., Meyer. Bar and cobar constructions. I. J. Pure Appl. Algebra, 33(2):163–207, 1984.Google Scholar
[63] J. R., Munkres. Topology: A first course. Prentice Hall, Englewood Cliffs, NJ, 1975.Google Scholar
[64] M. C., Pedicchio and S., Solomini. On a “good” dense class of topological spaces. J. Pure Appl. Algebra, 24:287-295, 1986.Google Scholar
[65] D. G., Quillen. Homotopical algebra. Lecture Notes in Mathematics, vol. 43. Springer, Berlin, 1967.
[66] A., Radulescu-Banu. Cofibrance and completion. PhD thesis, Massachusetts Institute of Technology. arXiv:0612.203. [math.AT], 1999.Google Scholar
[67] G., Raptis. Homotopy theory of posets. Homology, Homotopy Appl., 12(2):211–230, 2010.Google Scholar
[68] C. L., Reedy. Homotopy theory of model categories. Unpublished manuscript, available at the Hopf Topology Archive, ftp://hopf.math.purdue.edu/pub/Reedy/reedy.dvi, 1974.Google Scholar
[69] C., Rezk, S., Schwede, and B., Shipley. Simplicial structures on model categories and functors. Amer. J. Math., 123(3):551–575, 2001.Google Scholar
[70] E., Riehl. A model structure for quasi-categories. Unpublished expository manuscript, available at http://www.math.harvard.edu/~eriehl, 2008.Google Scholar
[71] E., Riehl. Algebraic model structures. New York J. Math., 17:173-231, 2011.Google Scholar
[72] E., Riehl. On the structure of simplicial categories associated to quasi-categories. Math. Proc. Cambridge Philos. Soc., 150(3):489–504, 2011.Google Scholar
[73] E., Riehl. Monoidal algebraic model structures. J. Pure Appl. Algebra, 217(6):1069–1104, 2013.Google Scholar
[74] E., Riehl and D. R. B., Verity. The 2-category theory of quasi-categories. Preprint, arXiv:1306.5144. [math.CT], 2013.Google Scholar
[75] E., Riehl and D. R. B., Verity. Homotopy coherent adjunctions and the formal theory of monads. Preprint, arXiv:1310.8279. [math.CT], 2013.Google Scholar
[76] E., Riehl and D. R. B., Verity. The theory and practice of Reedy categories. Preprint, arXiv:1304.6871. [math.CT], 2013.Google Scholar
[77] G., Segal. Configuration-spaces and iterated loop-spaces. Invent. Math., 21:213-221, 1973.Google Scholar
[78] G., Segal. Categories and cohomology theories. Topology, 13:293-312, 1974.Google Scholar
[79] M., Shulman. Homotopy limits and colimits and enriched homotopy theory. Preprint, arXiv:math/0610194. [math.AT], 2009.Google Scholar
[80] M., Shulman. Comparing composites of left and right derived functors. New York J. Math., 17:75-125, 2011.Google Scholar
[81] N. E., Steenrod. A convenient category of topological spaces. Michigan Math. J., 14:133-152, 1967.Google Scholar
[82] A., Strøm. The homotopy category is a homotopy category. Arch. Math. (Basel), 23:435-441, 1972.Google Scholar
[83] D., Sullivan. Geometric topology. Part I. Massachusetts Institute of Technology, Cambridge, MA, 1971. Localization, periodicity, and Galois symmetry, revised version.Google Scholar
[84] W. P., Thurston. On proof and progress in mathematics. Bull. Amer. Math. Soc. (N.S.), 30(2):161–177, 1994.Google Scholar
[85] D. R. B., Verity. Enriched categories, internal categories and change of base. Repr. Theory Appl. Categ., (20):1-266, 1992.Google Scholar
[86] D. R. B., Verity. Weak complicial sets. I. Basic homotopy theory. Adv. Math., 219(4):1081–1149, 2008.Google Scholar
[87] R. M., Vogt. Convenient categories of topological spaces for homotopy theory. Arch. Math. (Basel), 22:545-555, 1971.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Bibliography
  • Emily Riehl, Harvard University, Massachusetts
  • Book: Categorical Homotopy Theory
  • Online publication: 05 June 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781107261457.020
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Bibliography
  • Emily Riehl, Harvard University, Massachusetts
  • Book: Categorical Homotopy Theory
  • Online publication: 05 June 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781107261457.020
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Bibliography
  • Emily Riehl, Harvard University, Massachusetts
  • Book: Categorical Homotopy Theory
  • Online publication: 05 June 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781107261457.020
Available formats
×