Maps and localizations in the category of Segal spaces

The category of Segal spaces was proposed by Charles Rezk in 2000 as a suitable candidate for a model category for homotopy theories. We show that Quillen functors induce morphisms in this category and that the morphisms induced by Quillen pairs are "adjoint" in a useful sense. Quillen's original total derived functors are then obtained as a suitable localization of these morphisms within the category of Segal spaces. As an application, we consider a construction of "homotopy fibres" within a homotopy theory modelled by a Segal space and show that the homotopy fibre of a map is preserved by a localization which remembers only the homotopy category plus the automorphism groups of objects.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2005

Author dc:creator

• Robinson, Hugh Michael, 1978-

Advisor dc:contributor.advisor

• Haynes R. Miller.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

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

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/28923

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/28923