Parametrized higher category theory

We develop foundations for the category theory of [infinity]-categories parametrized by a base occategory. Our main contribution is a theory of parametrized homotopy limits and colimits, which recovers and extends the Dotto-Moi theory of G-colimits for G a finite group when the base is chosen to be the orbit category of G. We apply this theory to show that the G-[infinity]-category of G-spaces is freely generated under G-colimits by the contractible G-space, thereby affirming a conjecture of Mike Hill.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2017

Author dc:creator

• Shah, Jay (Jay Hungfai Gautam)

Advisor dc:contributor.advisor

• Clark Barwick.

• Mathematics.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/112894

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/112894