2026-09-20T07:02:46Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/289232022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Haynes R. Miller.
Robinson, Hugh Michael, 1978-
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2005-09-27T19:05:11Z
2005-09-27T19:05:11Z
2005
2005
http://hdl.handle.net/1721.1/28923
60503825
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
Includes bibliographical references (p. 30).
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.
by Hugh Michael Robinson.
Ph.D.
30 p.
1413482 bytes
1414195 bytes
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Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Maps and localizations in the category of Segal spaces
Thesis
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