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Categorical Methods in Algebra and Topology (CatMAT 2000)
August 21-25, 2000
University of Bremen
Bremen, Germany

Organizers
Hans-E. Porst, Horst Herrlich

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A Fibrewise Theory in Convenient Categories
by
Kyung Chan Min
Department of Mathematics, Yonsei University, Seoul, South Korea
Coauthors: Young Sun Kim (Paichai University), Jin Won Park (Cheju National University)

In homotopy theory it is convenient to work with a class of spaces which is closed under the standard operations of the theory and yet is large enough to contain all the spaces which are usually considered interesting. In fibrewise homotopy theory, there is a similar need to define a sufficiently extensive class of fibrewise spaces.

In this talk we start with a quasitopos providing a convenient setting for fibrewise spaces. In a quasitopos, we introduce various types of fibrewise exponential laws for spaces over various base spaces. In homotopy theory, exponential laws play an important role in the fibrations. Using fibrewise exponential laws, we give a systematic procedure for developing some important results related to the covering homotopy property.

Date received: June 23, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeq-52.