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Some phenomena in homotopical algebra


Author: K. Varadarajan
Journal: Proc. Amer. Math. Soc. 43 (1974), 272-276
MSC: Primary 55D40
DOI: https://doi.org/10.1090/S0002-9939-1974-0377870-3
MathSciNet review: 0377870
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Abstract: In [6] D. G. Quillen developed homotopy theory in categories satisfying certain axioms. He showed that many results in classical homotopy theory (of topological spaces) go through in his axiomatic set-up. The duality observed by Eckmann-Hilton in classical homotopy theory is reflected in the axioms of a model category. In [7] we developed the theory of numerical invariants like the Lusternik-Schnirelmann category and cocategory etc. for such model categories and in [8] we dealt with applications of this theory to injective and projective homotopy theory of modules as developed by Hilton [2], [3, Chapter 13].

Contrary to the general expectations there are many aspects of classical homotopy theory which cannot be carried over to Quillen's axiomatic set-up. This paper deals with some of these phenomena.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0377870-3
Keywords: Category, cocategory, $ p$-homotopy, $ i$-homotopy, Moore spaces
Article copyright: © Copyright 1974 American Mathematical Society

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