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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barwick, C.: From operator categories to topological operads (2013). Preprint. arXiv:1302.5756
Barwick, C., Glasman, S.: On the fibrewise effective Burnside ∞-category (2016). Preprint available from arXiv:1607.02786
Barwick, C., Dotto, E., Glasman, S., Nardin, D., Shah, J.: Elements of parametrized higher category theory (2016). Preprint available from arXiv:1608.03657.
Barwick, C., Glasman, S., Shah, J.: Spectral Mackey functors and equivariant algebraic K-theory (II) (2015). Preprint. arXiv:1505.03098
Dugger, D., Spivak, D.I.: Rigidification of quasi-categories. Algebr. Geom. Topol. 11(1), 225–261 (2011)
Gepner, D., Haugseng, R., Nikolaus, Th.: Lax colimits and free fibrations in ∞-categories (2015). Preprint. arXiv:1501.02161
Heuts, G., Moerdijk, I.: Left fibrations and homotopy colimits (2016). Preprint available from arXiv:1308.0704
Heuts, G., Moerdijk, I.: Left fibrations and homotopy colimits II (2016). Preprint available from arXiv:1602.01274
Hovey, M.: Model Categories, vol. 63 American Mathematical Society, Providence, RI (1999)
Lurie, J.: Higher Topos Theory. Annals of Mathematics Studies, vol. 170. Princeton University Press, Princeton, NJ (2009). MR 2522659 (2010j:18001)
Lurie, J.: (∞, 2)-categories and the Goodwillie calculus I. Preprint from the web page of the author (2009)
Lurie, J.: Derived algebraic geometry X. Formal moduli problems. Preprint from the web page of the author (2011)
Lurie, J.: Higher algebra. Preprint from the web page of the author (2012)
Stevenson, D.: Covariant model structures and simplicial localization (2016). Preprint. arXiv:1512.04815
Street, R.: Powerful functors. Preprint from the web page of the author (2001)
Acknowledgements
We are thankful to Bob Bruner, Emily Riehl, and the anonymous referee for their helpful comments on this paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Barwick, C., Shah, J. (2018). Fibrations in ∞-Category Theory. In: de Gier, J., Praeger, C., Tao, T. (eds) 2016 MATRIX Annals. MATRIX Book Series, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-72299-3_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-72299-3_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-72298-6
Online ISBN: 978-3-319-72299-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)