Skip to main content Accessibility help
×
Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T13:11:36.223Z Has data issue: false hasContentIssue false

Bibliography

Published online by Cambridge University Press:  25 April 2019

Denis-Charles Cisinski
Affiliation:
Universität Regensburg, Germany
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2019

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

[AFR17] Ayala, David, Francis, John, and Rozenblyum, Nick, A stratified homotopy hypothesis, preprint, arXiv: 1502.01713v4, 2017.Google Scholar
[Ara14] Ara, Dimitri, Higher quasi-categories vs higher Rezk spaces, J. K-Theory 14 (2014), no. 3, 701749. MR 3350089Google Scholar
[Bar16] Barwick, Clark, On the algebraic K-theory of higher categories, J. Topol. 9 (2016), no. 1, 245347. MR 3465850Google Scholar
[Ber07] Bergner, Julia E., Three models for the homotopy theory of homotopy theories, Topology 46 (2007), no. 4, 397–436. MR 2321038Google Scholar
[Ber12] Bergner, Julia E., Homotopy limits of model categories and more general homotopy theories, Bull. Lond. Math. Soc. 44 (2012), no. 2, 311–322. MR 2914609Google Scholar
[Ber18] Bergner, Julia E., The homotopy theory of (∞, 1)-categories, London Mathematical Society Student Texts, vol. 90, Cambridge University Press, Cambridge, 2018.CrossRefGoogle Scholar
[BHH17] Barnea, Ilan, Harpaz, Yonatan, and Horel, Geoffroy, Pro-categories in homotopy theory, Algebr. Geom. Topol. 17 (2017), no. 1, 567–643. MR 3604386Google Scholar
[BK12a] Barwick, Clark and Kan, Daniel M., A characterization of simplicial localization functors and a discussion of DK equivalences, Indag. Math. (N.S.) 23 (2012), no. 1–2, 69–79. MR 2877402Google Scholar
[BK12b] Barwick, Clark and Kan, Daniel M., Relative categories: another model for the homotopy theory of homotopy theories, Indag. Math. (N.S.) 23 (2012), no. 1–2, 42–68. MR 2877401Google Scholar
[BM11] Blumberg, Andrew J. and Mandell, Michael A., Algebraic K-theory and abstract homotopy theory, Adv. Math. 226 (2011), no. 4, 3760–3812. MR 2764905Google Scholar
[BR13] Bergner, Julia E. and Rezk, Charles, Reedy categories and the Θ-construction, Math. Z. 274 (2013), no. 1–2, 499–514. MR 3054341Google Scholar
[Bro73] Brown, Kenneth S., Abstract homotopy theory and generalized sheaf cohomology, Trans. Amer. Math. Soc. 186 (1973), 419–458. MR 0341469Google Scholar
[BS10] Baez, John C. and Shulman, Michael, Lectures on n-categories and cohomology, Towards higher categories, IMA Volumes in Mathematics and its Applications, vol. 152, Springer, New York, 2010, pp. 1–68. MR 2664619CrossRefGoogle Scholar
[BV73] Boardman, J. Michael and Vogt, Rainer M., Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics, vol. 347, Springer, Berlin, 1973. MR 0420609CrossRefGoogle Scholar
[Cis06] Cisinski, Denis-Charles, Les préfaisceaux comme modèles des types d’homotopie, Astérisque (2006), no. 308, xxiv+392. MR 2294028Google Scholar
[Cis08] Cisinski, Denis-Charles, Propriétés universelles et extensions de Kan dérivées, Theory Appl. Categ. 20 (2008), no. 17, 605–649. MR 2534209Google Scholar
[Cis09] Cisinski, Denis-Charles, Locally constant functors, Math. Proc. Cambridge Philos. Soc. 147 (2009), no. 3, 593–614. MR 2557145Google Scholar
[Cis10] Cisinski, Denis-Charles, Catégories dérivables, Bull. Soc. Math. France 138 (2010), no. 3, 317– 393. MR 2729017Google Scholar
[Cis16] Cisinski, Denis-Charles, Catégories supérieures et théorie des topos, Astérisque (2016), no. 380, Séminaire Bourbaki, vol. 2014/2015, Exp. No. 1097, 263–324. MR 3522177Google Scholar
[DHKS04] Dwyer, William G., Hirschhorn, Philip S., Kan, Daniel M., and Smith, Jeffrey H., Homotopy limit functors on model categories and homotopical categories, Mathematical Surveys and Monographs, vol. 113, American Mathematical Society, Providence, RI, 2004. MR 2102294Google Scholar
[DK80a] Dwyer, William G. and Kan, Daniel M., Calculating simplicial localizations, J. Pure Appl. Algebra 18 (1980), no. 1, 17–35. MR 578563Google Scholar
[DK80b] Dwyer, William G. and Kan, Daniel M., Function complexes in homotopical algebra, Topology 19 (1980), no. 4, 427–440. MR 584566Google Scholar
[DK80c] Dwyer, William G. and Kan, Daniel M., Simplicial localizations of categories, J. Pure Appl. Algebra 17 (1980), no. 3, 267–284. MR 579087Google Scholar
[DK87] Dwyer, William G. and Kan, Daniel M., Equivalences between homotopy theories of diagrams, Algebraic topology and algebraic K-theory (Princeton, NJ, 1983), Annals of Mathematics Studies, vol. 113, Princeton University Press, Princeton, NJ, 1987, pp. 180– 205. MR 921478Google Scholar
[DS11] Dugger, Daniel and Spivak, David I., Mapping spaces in quasi-categories, Algebr. Geom. Topol. 11 (2011), no. 1, 263–325. MR 2764043Google Scholar
[Dug01a] Dugger, Daniel, Combinatorial model categories have presentations, Adv. Math. 164 (2001), no. 1, 177–201. MR 1870516Google Scholar
[Dug01b] Dugger, Daniel, Universal homotopy theories, Adv. Math. 164 (2001), no. 1, 144–176. MR 1870515Google Scholar
[Fre70] Freyd, Peter, Homotopy is not concrete, The Steenrod algebra and its applications (Proc. Conf. to celebrate N. E. Steenrod’s sixtieth birthday, Battelle Memorial Inst., Columbus, Ohio, 1970), Lecture Notes in Mathematics, vol. 168, Springer, Berlin, 1970, pp. 25–34. MR 0276961CrossRefGoogle Scholar
[GJ99] Goerss, Paul G. and Jardine, John F., Simplicial homotopy theory, Progress in Mathematics, vol. 174, Birkhäuser, Basel, 1999. MR 1711612CrossRefGoogle Scholar
[GZ67] Gabriel, Pierre and Zisman, Michel, Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35, Springer, New York, 1967. MR 0210125CrossRefGoogle Scholar
[HM15] Heuts, Gijs and Moerdijk, Ieke, Left fibrations and homotopy colimits, Math. Z. 279 (2015), no. 3–4, 723–744. MR 3318247Google Scholar
[Hor16] Horel, Geoffroy, Brown categories and bicategories, Homology Homotopy Appl. 18 (2016), no. 2, 217–232. MR 3575996Google Scholar
[Hov99] Hovey, Mark, Model categories, Mathematical Surveys and Monographs, vol. 63, American Mathematical Society, Providence, RI, 1999. MR 1650134Google Scholar
[Hoy17] Hoyois, Marc, The six operations in equivariant motivic homotopy theory, Adv. Math. 305 (2017), 197–279. MR 3570135Google Scholar
[Joy02] Joyal, André, Quasi-categories and Kan complexes, J. Pure Appl. Algebra 175 (2002), no. 1–3, 207–222, Special volume celebrating the 70th birthday of Professor Max Kelly. MR 1935979Google Scholar
[Joy08a] Joyal, André, Notes on quasi-categories, preprint, 2008.Google Scholar
[Joy08b] Joyal, André, The theory of quasi-categories and its applications, preprint, 2008.Google Scholar
[JT07] Joyal, André and Tierney, Myles, Quasi-categories vs Segal spaces, Categories in algebra, geometry and mathematical physics, Contemporary Mathematics, vol. 431, American Mathematical Society, Providence, RI, 2007, pp. 277–326. MR 2342834CrossRefGoogle Scholar
[Kan58] Kan, Daniel M., Adjoint functors, Trans. Amer. Math. Soc. 87 (1958), 294– 329. MR 0131451Google Scholar
[Kap17] Kapulkin, Krzysztof, Locally cartesian closed quasi-categories from type theory, J. Topol. 10 (2017), no. 4, 1029–1049. MR 3743067Google Scholar
[KL16] Kapulkin, Krzysztof and Lumsdaine, Peter Lefanu, The simplicial model of univalent foundations (after Voevodsky), preprint, arXiv: 1211.2851, 2016.Google Scholar
[KM08] Kahn, Bruno and Maltsiniotis, Georges, Structures de dérivabilité, Adv. Math. 218 (2008), no. 4, 1286–1318. MR 2419385Google Scholar
[Lei14] Leinster, Tom, Basic category theory, Cambridge Studies in Advanced Mathematics, vol. 143, Cambridge University Press, Cambridge, 2014. MR 3307165CrossRefGoogle Scholar
[Len18] Lenz, Tobias, Homotopy (pre-)derivators of cofibration categories and quasi-categories, preprint, arXiv: 1712.07845; to appear in Algebr. Geom. Topol., 2018.Google Scholar
[LMG15] Low, Zhen Lin and Mazel-Gee, Aaron, From fractions to complete Segal spaces, Homology Homotopy Appl. 17 (2015), no. 1, 321–338. MR 3350085Google Scholar
[Lur09] Lurie, Jacob, Higher topos theory, Annals of Mathematics Studies, vol. 170, Princeton University Press, Princeton, NJ, 2009. MR 2522659CrossRefGoogle Scholar
[Lur17] Lurie, Jacob, Higher algebra, Harvard University, Cambridge, MA, 2017.Google Scholar
[Mal05a] Maltsiniotis, Georges, La théorie de l’homotopie de Grothendieck, Astérisque (2005), no. 301, vi+140. MR 2200690Google Scholar
[Mal05b] Maltsiniotis, Georges, Structures d’asphéricité, foncteurs lisses, et fibrations, Ann. Math. Blaise Pascal 12 (2005), no. 1, 1–39, English translation available at arXiv: 0912.2432. MR 2126440Google Scholar
[Mal07] Maltsiniotis, Georges, Le théorème de Quillen, d’adjonction des foncteurs dérivés, revisité, C. R. Math. Acad. Sci. Paris 344 (2007), no. 9, 549–552. MR 2323740Google Scholar
[Mal12] Maltsiniotis, Georges, Carrés exacts homotopiques et dérivateurs, Cah. Topol. Géom. Différ. Catég. 53 (2012), no. 1, 3–63. MR 2951712Google Scholar
[Mei16] Meier, Lennart, Fibration categories are fibrant relative categories, Algebr. Geom. Topol. 16 (2016), no. 6, 3271–3300. MR 3584258Google Scholar
[MG16a] Mazel-Gee, Aaron, Goerss–Hopkins obstruction theory via model ∞-categories, Ph.D. thesis, University of California, Berkeley, 2016.Google Scholar
[MG16b] Mazel-Gee, Aaron, Quillen adjunctions induce adjunctions of quasicategories, New York J. Math. 22 (2016), 57–93. MR 3484677Google Scholar
[Mor06] Morel, Fabien, Homotopy theory of schemes, SMF/AMS Texts and Monographs, vol. 12, American Mathematical Society, Providence, RI; Société Mathématique de France, Paris, 2006, Translated from the 1999 French original by James D. Lewis. MR 2257774Google Scholar
[NB07] Nichols-Barrer, Joshua Paul, On quasi-categories as a foundation for higher algebraic stacks, Ph.D. thesis, Massachusetts Institute of Technology, 2007.Google Scholar
[Nik11] Nikolaus, Thomas, Algebraic models for higher categories, Indag. Math. (N.S.) 21 (2011), no. 1–2, 52–75. MR 2832482Google Scholar
[NRS18] Nguyen, Hoang Kim, Raptis, George, and Schrade, Christoph, Adjoint functor theorems for-categories, preprint, arXiv: 1803.01664, 2018.Google Scholar
[Nui16] Nuiten, Joost, Localizing-categories with hypercovers, preprint, arXiv: 1612.03800, 2016.Google Scholar
[Qui67] Quillen, Daniel G., Homotopical algebra, Lecture Notes in Mathematics, vol. 43, Springer, Berlin, 1967. MR 0223432CrossRefGoogle Scholar
[Qui73] Quillen, Daniel, Higher algebraic K-theory. I, Algebraic K-theory I, Lecture Notes in Mathematics, vol. 341, Springer, Berlin, 1973, pp. 85–147. MR 0338129CrossRefGoogle Scholar
[RB09] Rădulescu-Banu, Andrei, Cofibrations in homotopy theory, preprint, arXiv: math/0610009v4, 2009.Google Scholar
[Rez01] Rezk, Charles, A model for the homotopy theory of homotopy theory, Trans. Amer. Math. Soc. 353 (2001), no. 3, 973–1007. MR 1804411Google Scholar
[Rez10a] Rezk, Charles, A Cartesian presentation of weak n-categories, Geom. Topol. 14 (2010), no. 1, 521–571. MR 2578310Google Scholar
[Rez10b] Rezk, Charles, Correction to “A Cartesian presentation of weak n-categories”, Geom. Topol. 14 (2010), no. 4, 2301–2304. MR 2740648Google Scholar
[Rie14] Riehl, Emily, Categorical homotopy theory, New Mathematical Monographs, vol. 24, Cambridge University Press, Cambridge, 2014. MR 3221774CrossRefGoogle Scholar
[Rie17] Riehl, Emily, Category theory in context, Aurora: Dover Modern Math Originals, Dover Publications, Mineola, NY, 2017.Google Scholar
[RV16] Riehl, Emily and Verity, Dominic, Homotopy coherent adjunctions and the formal theory of monads, Adv. Math. 286 (2016), 802–888. MR 3415698Google Scholar
[RV17a] Riehl, Emily and Verity, Dominic, Fibrations and Yoneda’s lemma in an ∞-cosmos, J. Pure Appl. Algebra 221 (2017), no. 3, 499–564. MR 3556697Google Scholar
[RV17b] Riehl, Emily and Verity, Dominic, Kan extensions and the calculus of modules for ∞-categories, Algebr. Geom. Topol. 17 (2017), no. 1, 189–271. MR 3604377Google Scholar
[SGA72] Géométrie, Séminaire de Bois-Marie, Algébrique du 1963–1964 (SGA 4), Dirigé par M. Artin, A. Grothendieck, et J. L. Verdier. Avec la collaboration de N. Bourbaki, P. Deligne et B. Saint-Donat. Théorie des topos et cohomologie étale des schémas. Tome 1: Théorie des topos, Lecture Notes in Mathematics, vol. 269, Springer, Berlin, 1972. MR 0354652Google Scholar
[Shu08] Shulman, Michael, Set theory for category theory, preprint, arXiv: 0810.1279v2, 2008.Google Scholar
[Sim99] Simpson, Carlos, A Giraud-type characterization of the simplicial categories associated to closed model categories as ∞-pretopoi, preprint, arXiv: math/9903167, 1999.Google Scholar
[Sim12] Simpson, Carlos, Homotopy theory of higher categories, New Mathematical Monographs, vol. 19, Cambridge University Press, Cambridge, 2012. MR 2883823Google Scholar
[Spi10] Spitzweck, Markus, Homotopy limits of model categories over inverse index categories, J. Pure Appl. Algebra 214 (2010), no. 6, 769–777. MR 2580656Google Scholar
[Szu16] Szumiło, Karol, Homotopy theory of cofibration categories, Homology Homotopy Appl. 18 (2016), no. 2, 345–357. MR 3576003Google Scholar
[Szu17] Szumiło, Karol, Homotopy theory of cocomplete quasicategories, Algebr. Geom. Topol. 17 (2017), no. 2, 765–791. MR 3623671Google Scholar
[Tho79] Thomason, Robert W., Homotopy colimits in the category of small categories, Math. Proc. Cambridge Philos. Soc. 85 (1979), no. 1, 91–109. MR 510404Google Scholar
[Toë05] Toën, Bertrand, Vers une axiomatisation de la théorie des catégories supérieures, K-Theory 34 (2005), no. 3, 233–263. MR 2182378Google Scholar
[TV05] Toën, Bertrand and Vezzosi, Gabriele, Homotopical algebraic geometry. I. Topos theory, Adv. Math. 193 (2005), no. 2, 257–372. MR 2137288Google Scholar
[TV08] Toën, Bertrand and Vezzosi, Gabriele, Homotopical algebraic geometry. II. Geometric stacks and applications, Mem. Amer. Math. Soc. 193 (2008), no. 902, x+224. MR 2394633Google Scholar
[Uni13] The Univalent Foundations Program, Homotopy type theory – univalent foundations of mathematics, Institute for Advanced Study (IAS), Princeton, NJ, 2013. MR 3204653Google Scholar
[VK14] Varshavskiĭ, Ya. and Kazhdan, D., The Yoneda lemma for complete Segal spaces, Funktsional. Anal. i Prilozhen. 48 (2014), no. 2, 3–38, translation in Funct. Anal. Appl. 48 (2014), no. 2, 81–106. MR 3288174Google Scholar
[Wei99] Weiss, Michael, Hammock localization in Waldhausen categories, J. Pure Appl. Algebra 138 (1999), no. 2, 185–195. MR 1689629Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] 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
  • Denis-Charles Cisinski, Universität Regensburg, Germany
  • Book: Higher Categories and Homotopical Algebra
  • Online publication: 25 April 2019
  • Chapter DOI: https://doi.org/10.1017/9781108588737.009
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
  • Denis-Charles Cisinski, Universität Regensburg, Germany
  • Book: Higher Categories and Homotopical Algebra
  • Online publication: 25 April 2019
  • Chapter DOI: https://doi.org/10.1017/9781108588737.009
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
  • Denis-Charles Cisinski, Universität Regensburg, Germany
  • Book: Higher Categories and Homotopical Algebra
  • Online publication: 25 April 2019
  • Chapter DOI: https://doi.org/10.1017/9781108588737.009
Available formats
×