Some phenomena in homotopical algebra

Varadarajan, K.

doi:10.1090/S0002-9939-1974-0377870-3

Some phenomena in homotopical algebra
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by K. Varadarajan

Proc. Amer. Math. Soc. 43 (1974), 272-276

DOI: https://doi.org/10.1090/S0002-9939-1974-0377870-3

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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.

References

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Numerical invariants in homotopical algebra

Applications

K. Varadarajan, Groups for which Moore spaces $M(\pi ,\,1)$ exist, Ann. of Math. (2) 84 (1966), 368–371. MR 202143, DOI 10.2307/1970450