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On the homomorphisms of sequences

Published online by Cambridge University Press:  24 October 2008

W. H. Cockcroft
W. H. Cockcroft
Affiliation:
Department of MathamaticsKing's CollegeAberdeen
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Extract

The algebraic classification problem with which I shall be concerned in this paper is suggested by the algebraic theory of homomorphisms of free crossed modules whose groups of operators are free groups. This theory arises in the study of the homotopy theory of two-dimensional C.W. complexes*. It is shown in (3) that the homotopy theory of such complexes, including the homotopy classification of mappings, is equivalent to this purely algebraic theory.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 48 , Issue 4 , October 1952 , pp. 521 - 532
Copyright
Copyright © Cambridge Philosophical Society 1952

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References

REFERENCES

(1)Maclane, S.Cohomology theory in abstract groups. III. Ann. Math., Princeton (2), 50 (1949), 736.Google Scholar
(2)Maclane, S. and Whitehead, J. H. C.On the 3-type of a complex. Proc. nat. Acad. Sci., Wash., 36 (1950), 41.Google Scholar
(3)Whitehead, J. H. C.Combinatorial homotopy, II. Bull. Amer. math. Soc. 55 (1949), 453.Google Scholar