Fibrations in -Category Theory

Chapter
Part of the MATRIX Book Series book series (MXBS, volume 1)

Abstract

In this short expository note, we discuss, with plenty of examples, the bestiary of fibrations in quasicategory theory. We underscore the simplicity and clarity of the constructions these fibrations make available to end-users of higher category theory.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

We are thankful to Bob Bruner, Emily Riehl, and the anonymous referee for their helpful comments on this paper.

References

  1. 1.
    Barwick, C.: From operator categories to topological operads (2013). Preprint. arXiv:1302.5756Google Scholar
  2. 2.
    Barwick, C., Glasman, S.: On the fibrewise effective Burnside -category (2016). Preprint available from arXiv:1607.02786Google Scholar
  3. 3.
    Barwick, C., Dotto, E., Glasman, S., Nardin, D., Shah, J.: Elements of parametrized higher category theory (2016). Preprint available from arXiv:1608.03657.Google Scholar
  4. 4.
    Barwick, C., Glasman, S., Shah, J.: Spectral Mackey functors and equivariant algebraic K-theory (II) (2015). Preprint. arXiv:1505.03098Google Scholar
  5. 5.
    Dugger, D., Spivak, D.I.: Rigidification of quasi-categories. Algebr. Geom. Topol. 11(1), 225–261 (2011)Google Scholar
  6. 6.
    Gepner, D., Haugseng, R., Nikolaus, Th.: Lax colimits and free fibrations in -categories (2015). Preprint. arXiv:1501.02161Google Scholar
  7. 7.
    Heuts, G., Moerdijk, I.: Left fibrations and homotopy colimits (2016). Preprint available from arXiv:1308.0704Google Scholar
  8. 8.
    Heuts, G., Moerdijk, I.: Left fibrations and homotopy colimits II (2016). Preprint available from arXiv:1602.01274Google Scholar
  9. 9.
    Hovey, M.: Model Categories, vol. 63 American Mathematical Society, Providence, RI (1999)Google Scholar
  10. 10.
    Lurie, J.: Higher Topos Theory. Annals of Mathematics Studies, vol. 170. Princeton University Press, Princeton, NJ (2009). MR 2522659 (2010j:18001)Google Scholar
  11. 11.
    Lurie, J.: (, 2)-categories and the Goodwillie calculus I. Preprint from the web page of the author (2009)Google Scholar
  12. 12.
    Lurie, J.: Derived algebraic geometry X. Formal moduli problems. Preprint from the web page of the author (2011)Google Scholar
  13. 13.
    Lurie, J.: Higher algebra. Preprint from the web page of the author (2012)Google Scholar
  14. 14.
    Stevenson, D.: Covariant model structures and simplicial localization (2016). Preprint. arXiv:1512.04815Google Scholar
  15. 15.
    Street, R.: Powerful functors. Preprint from the web page of the author (2001)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations