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Numerical Invariants in Homotopical Algebra, I

Published online by Cambridge University Press:  20 November 2018

K. Varadarajan
K. Varadarajan*
Affiliation:
University of Calgary, Calgary, Alberta
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Classically CW-complexes were found to be the best suited objects for studying problems in homotopy theory. Certain numerical invariants associated to a CW-complex X such as the Lusternik-Schnirelmann Category of X, the index of nilpotency of ᘯ(X), the cocategory of X, the index of conilpotency of ∑ (X) have been studied by Eckmann, Hilton, Berstein and Ganea, etc. Recently D. G. Quillen [6] has developed homotopy theory for categories satisfying certain axioms. In the axiomatic set up of Quillen the duality observed in classical homotopy theory becomes a self-evident phenomenon, the axioms being so formulated.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 4 , 01 August 1975 , pp. 901 - 934
Copyright
Copyright © Canadian Mathematical Society 1975

References

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