Abstract homotopy theory and homotopy theory of functor category (Q913943)
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scientific article; zbMATH DE number 4148384
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Abstract homotopy theory and homotopy theory of functor category |
scientific article; zbMATH DE number 4148384 |
Statements
Abstract homotopy theory and homotopy theory of functor category (English)
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1989
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The author studies an axiomatization of homotopy theories and deduces various fundamental theorems in a systematic manner [cf. \textit{K. H. Kamps}, Math. Z. 124, 215-236 (1972; Zbl 0223.55020) and \textit{T. Matumoto}, J. Fac. Sci., Univ. Tokyo, Sect. I A 18, 363-374 (1971; Zbl 0232.57031)]. Puppe's theorem and J. H. C. Whitehead's theorem etc. hold in the category of functor complexes. Moreover, obstruction theory and Postnikov systems in the functor category are developed.
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abstract homotopy category
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cylinder and path functors
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Eilenberg-MacLane \({\mathcal F}\)-space
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axiomatization of homotopy theories
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category of functor complexes
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obstruction theory
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Postnikov systems
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