David Spivak

Research Scientist
Department of Mathematics

Email: dspivak--math/mit/edu

Our research:

The following joint research with Professor Dan Dugger was undertaken while I was a postdoc at the University of Oregon (2007-2010).

Rigidification of quasi-categories. Here we prove that the mapping space between two objects in the rigidification of a quasi-category is isomorphic to the nerve of the category of necklaces connecting those two objects. On the arXiv.

Mapping spaces in quasi-categories. Here we prove that the mapping spaces in a quasi-category are as one who is familiar with the homotopy mapping complexes of Dwyer-Kan might expect. We prove that various formulations of these mapping spaces found in Lurie's book HTT can all be obtained in this way. Finally we give a self-contained proof of Lurie's result that the Joyal model structure on simplicial sets is Quillen equivalent to Bergner's model structure on simplicial categories. On the arXiv.

Some related research:

Jacob Lurie Higher Topos Theory.

Emily Riehl On the structure of simplicial categories associated to quasi-categories.

Josh Nichols-Barrer Combinatorial Quasi-Categories (Thesis Chapters 1 and 2).

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This work by David I. Spivak is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License.