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Coretraction-fibrations are retractions

Published online by Cambridge University Press:  17 April 2009

E. Chislett  and
C.S. Hoo
E. Chislett
Affiliation:
University of Alberta, Edmonton, Alberta, Canada.
C.S. Hoo
Affiliation:
University of Alberta, Edmonton, Alberta, Canada.
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Abstract

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We prove that if C is an abelian category and M is the class of all coretractions, then the class of M-fibrations is the class of all retractions. As a corollary we prove that the class of all retractions is contained in the class of M-fibrations for any M.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 3 , December 1971 , pp. 363 - 374
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Bauer, F.-W. and Dugundji, J., “Categorical homotopy and fibrations”, Trans. Amer. Math. Soc. 140 (1969), 239–256.CrossRefGoogle Scholar
[2]Gabriel, P. and Zisman, M., Calculus of fractions and homotopy theory (Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35. Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
[3]Hilton, Peter, Homotopy theory and duality (Gordon and Breach, New York, London, 1965).Google Scholar
[4]Pressman, Irwin S., “Obstructions to liftings in commutative squares”, (Preprint, Ohio State University, 1970).Google Scholar
[5]Ringel, Claus Michael, “Faserungen und Homotopie in Kategorien”, Math. Ann. 190 (1971), 215–230.CrossRefGoogle Scholar