@article {Mukherjee, AUTHOR = {Chirantan Mukherjee and Nima Rasekh}, TITLE = {Twisted Arrow Construction for Segal Spaces}, YEAR = {2022}, JOURNAL = {arXiv preprint}, NOTE = {arXiv:2203.01788v1}, }

@phdthesis{ author={Mukherjee,Chirantan}, year={2022}, title={Complete Segal Spaces as a Model of Higher Categories}, journal={ProQuest Dissertations and Theses}, pages={117}, note={Copyright - Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works; Last updated - 2022-06-22}, abstract={This thesis aims to define an important model of $(\infty,1)-$categories, namely the complete Segal spaces, and understand the necessary foundations needed to define it. We achieve this in several steps. First, we review categorical homotopy theory. Then we study the theory of model categories and give a detailed characterization of the Kan model structure on simplicial sets. We then focus on understanding Reedy fibrant simplicial spaces, the Segal condition and its relation to the composition of maps, and how it is used to define Segal spaces. This is followed by appending the importance of the completeness condition via Dwyer-Kan equivalences. Next we define the twisted arrow construction for simplicial spaces, and show that the twisted arrow construction of a complete Segal space X, Tw(X) is a complete Segal space. Further, we show that the projection map Tw(X) → Xop x X is a left fibration of the complete Segal space.}, keywords={Category Theory; Complete Segal Spaces; Fibrations; Higher Category Theory; Homotopy Theory; Segal Spaces; Mathematics; 0405:Mathematics}, isbn={9798438788232}, language={English}, url={https://www.lib.uwo.ca/cgi-bin/ezpauthn.cgi?url=http://search.proquest.com/dissertations-theses/complete-segal-spaces-as-model-higher-categories/docview/2666561440/se-2}, }