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Categorical Fibrations

Published online by Cambridge University Press:  20 November 2018

Ulrich Seip
Ulrich Seip*
Affiliation:
University of Ottawa
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Extract

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If one considers the theories of Hurewicz, - Serre - or other fibrations in the categories of topological or pointed topological spaces, one can see that many of the fundamental theorems can be formulated and proven in the general case of categories for which certain functors and natural transformations are given. And, since fibrations may be defined either by a cylinder or a path space construction, we shall give in an analogous way two different definitions of fibrations in the general case.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 1 , April 1967 , pp. 5 - 17
Copyright
Copyright © Canadian Mathematical Society 1967

Footnotes

1

The author holds an NRC fellowship

References

1. Dugundji, J., Topology. Allyn and Bacon, Boston (1966).Google Scholar
2. Hu, S-T., Homotopy Theory. Academic Press, New York (1955).Google Scholar
3. Kan, D. M., Abstract Homotopy IL Proc. Nat. Acad. Sci. U. S. A. 42 (1955).Google Scholar
4. Kan, D. M., Adjoint Functors. Trans. A. M. S. 87 (1955).Google Scholar