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Macquarie University  Department of Mathematics

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Workshop on Categorical Methods in Algebra, Geometry and Mathematical Physics

Satellite to the StreetFest conference in honour of Ross Street's sixtieth birthday

July 18-21 2005, Australian National University, Canberra

Mon, 18 July:  15:50 - 16:30

Some localizations of Segal spaces
Robinson, Hugh (Australian National University)

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.

Typeset PDF of this abstract.