Maps and localizations in the category of Segal spaces
Author(s)Robinson, Hugh Michael, 1978-
Massachusetts Institute of Technology. Dept. of Mathematics.
Haynes R. Miller.
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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.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.Includes bibliographical references (p. 30).
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology