Algebra and Topology Seminar

4pm Tuesday 05 April 2005
Hugh Robinson
MSI

Some localizations 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. Quillen functors induce morphisms in this category and 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.

We also consider a construction of "homotopy fibres" within a pointed homotopy theory modelled by a Segal space. Then the homotopy fibre of a map is preserved by a similar localization which remembers only the homotopy category plus the automorphism groups of objects.




Return to list of seminars