Maps and localizations in the category of Segal spaces
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...
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ndltd-MIT-oai-dspace.mit.edu-1721.1-289232019-05-02T16:14:23Z Maps and localizations in the category of Segal spaces Robinson, Hugh Michael, 1978- Haynes R. Miller. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. 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. 2005-09-27T19:05:11Z 2005-09-27T19:05:11Z 2005 2005 Thesis http://hdl.handle.net/1721.1/28923 60503825 en_US 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. http://dspace.mit.edu/handle/1721.1/7582 30 p. 1413482 bytes 1414195 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
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Mathematics. Robinson, Hugh Michael, 1978- Maps and localizations in the category of Segal spaces |
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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. |
author2 |
Haynes R. Miller. |
author_facet |
Haynes R. Miller. Robinson, Hugh Michael, 1978- |
author |
Robinson, Hugh Michael, 1978- |
author_sort |
Robinson, Hugh Michael, 1978- |
title |
Maps and localizations in the category of Segal spaces |
title_short |
Maps and localizations in the category of Segal spaces |
title_full |
Maps and localizations in the category of Segal spaces |
title_fullStr |
Maps and localizations in the category of Segal spaces |
title_full_unstemmed |
Maps and localizations in the category of Segal spaces |
title_sort |
maps and localizations in the category of segal spaces |
publisher |
Massachusetts Institute of Technology |
publishDate |
2005 |
url |
http://hdl.handle.net/1721.1/28923 |
work_keys_str_mv |
AT robinsonhughmichael1978 mapsandlocalizationsinthecategoryofsegalspaces |
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1719036816016801792 |