Skip to main content
SpringerLink
Log in

2-Segal Spaces from Higher Categories

  • Chapter
  • First Online:
Higher Segal Spaces

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2244))

Abstract

All simplicial spaces in this section will be combinatorial, i.e., objects of \({{\mathbb S}}_{\Delta }\).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bondal, A.I., Kapranov, M.M.: Enhanced triangulated categories. Math. Sb. 181, 669–683 (1990)

    MATH  Google Scholar 

  2. Dwyer, W.G., Kan, D.M.: Calculating simplicial localizations. J. Pure Appl. Algebra 18(1), 17–35 (1980)

    Article  MathSciNet  Google Scholar 

  3. Dwyer, W.G., Kan, D.M.: Function complexes in homotopical algebra. Topology 19(4), 427–440 (1980)

    Article  MathSciNet  Google Scholar 

  4. Dwyer, W.G., Kan, D.M.: Simplicial localizations of categories. J. Pure Appl. Algebra 17(3), 267–284 (1980)

    Article  MathSciNet  Google Scholar 

  5. Drinfeld, V.: On the notion of geometric realization. Moscow Math. J. 4(3), 619–626 (2004)

    Article  MathSciNet  Google Scholar 

  6. Hinich, V.: Homological algebra of homotopy algebras. Commun. Algebra 25(10), 3291–3323 (1997)

    Article  MathSciNet  Google Scholar 

  7. Joyal, A.: 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 

  8. Joyal, A., Tierney, M.: Quasi-categories vs Segal spaces. In: Categories in Algebra, Geometry and Mathematical Physics. Contemporary Mathematics, vol. 431, pp. 277–326. American Mathematical Society, Providence (2007)

    Google Scholar 

  9. Kontsevich, M., Soibelman, Y.: Notes on A ∞-algebras, A ∞-categories and non-commutative geometry. In: Homological Mirror Symmetry. Lecture Notes in Physics, vol. 757, pp. 153–219. Springer, Berlin (2009)

    Google Scholar 

  10. Lurie, J.: Higher Topos Theory. Annals of Mathematics Studies, vol. 170. Princeton University Press, Princeton (2009)

    Google Scholar 

  11. Lurie, J.: Higher algebra. 2014, preprint, available at http://www.math.harvard.edu/~lurie (2016)

  12. Rezk, C.: A model for the homotopy theory of homotopy theory. Trans. Am. Math. Soc. 353(3), 973–1007 (2001)

    Article  MathSciNet  Google Scholar 

  13. Tabuada, G.: Une structure de catégorie de modèles de Quillen sur la catégorie des dg-catégories. C. R. Math. Acad. Sci. Paris 340(1), 15–19 (2005)

    Article  MathSciNet  Google Scholar 

  14. Toën, B.: Derived Hall algebras. Duke Math. J. 135(3), 587–615 (2006)

    Article  MathSciNet  Google Scholar 

  15. Toën, B.: The homotopy theory of dg-categories and derived Morita theory. Invent. Math. 167(3), 615–667 (2007)

    Article  MathSciNet  Google Scholar 

  16. Toën, B., Vaquié, M.: Moduli of objects in dg-categories. Ann. Sci. École Norm. Sup. 40(3), 387–444 (2007)

    Article  MathSciNet  Google Scholar 

  17. Waldhausen, F.: Algebraic K-theory of spaces. In: Algebraic and Geometric Topology, pp. 318–419 (1985)

    Google Scholar 

  18. Weibel, C.A.: An Introduction to Homological Algebra. Cambridge Studies in Advanced Mathematics, vol. 38. Cambridge University Press, Cambridge (1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Hamburg, Hamburg, Germany

    Tobias Dyckerhoff

  2. Kavli Institute for the Physics and Mathematics of the Universe, Kashiwa, Japan

    Mikhail Kapranov

Authors
  1. Tobias Dyckerhoff
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mikhail Kapranov
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Dyckerhoff, T., Kapranov, M. (2019). 2-Segal Spaces from Higher Categories. In: Higher Segal Spaces. Lecture Notes in Mathematics, vol 2244. Springer, Cham. https://doi.org/10.1007/978-3-030-27124-4_7

Download citation

Publish with us

Policies and ethics

Search

Navigation