| dc.contributor.advisor | Clark Barwick. | en_US |
| dc.contributor.author | Shah, Jay (Jay Hungfai Gautam) | en_US |
| dc.contributor.other | Massachusetts Institute of Technology. Department of Mathematics. | en_US |
| dc.date.accessioned | 2017-12-20T18:16:23Z | |
| dc.date.available | 2017-12-20T18:16:23Z | |
| dc.date.copyright | 2017 | en_US |
| dc.date.issued | 2017 | en_US |
| dc.identifier.uri | http://hdl.handle.net/1721.1/112894 | |
| dc.description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2017. | en_US |
| dc.description | Cataloged from PDF version of thesis. | en_US |
| dc.description | Includes bibliographical references (page 99). | en_US |
| dc.description.abstract | 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. | en_US |
| dc.description.statementofresponsibility | by Jay Shah. | en_US |
| dc.format.extent | 99 pages | en_US |
| dc.language.iso | eng | en_US |
| dc.publisher | Massachusetts Institute of Technology | en_US |
| 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. | en_US |
| dc.rights.uri | http://dspace.mit.edu/handle/1721.1/7582 | en_US |
| dc.subject | Mathematics. | en_US |
| dc.title | Parametrized higher category theory | en_US |
| dc.type | Thesis | en_US |
| dc.description.degree | Ph. D. | en_US |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | |
| dc.identifier.oclc | 1015183712 | en_US |
