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Homotopy Theory in Abelian Categories

Published online by Cambridge University Press:  20 November 2018

Heinrich Kleisli
Heinrich Kleisli*
Affiliation:
Battelle Memorial Institute, Geneva
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The concept of homotopy for homomorphisms of modules, suggested by analogy with fundamental properties of the topological homotopy, was developed by Eckmann and Hilton (3; 9; 10). In the present paper, this concept of homotopy is generalized to additive categories with an additional structure, and the theory of homotopy, including in particular various exact homotopy sequences, is established in full detail. It may be helpful to the reader to realize that most of our theorems, concepts, and constructions have their analogues in the homotopy theory of topological spaces. Many of these analogues may be found in a recent paper by Eckmann and Hilton (4). Explicit references will be given at various places in the paper.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 14 , 1962 , pp. 139 - 169
Copyright
Copyright © Canadian Mathematical Society 1962

References

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