Homotopy Theory of Diagrams

Homotopy Theory of Diagrams
Author :
Publisher : American Mathematical Soc.
Total Pages : 106
Release :
ISBN-10 : 9780821827598
ISBN-13 : 0821827596
Rating : 4/5 (596 Downloads)

Book Synopsis Homotopy Theory of Diagrams by : Wojciech Chachólski

Download or read book Homotopy Theory of Diagrams written by Wojciech Chachólski and published by American Mathematical Soc.. This book was released on 2002 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors develop homotopy theoretical methods for studying diagrams. In particular they explain how to construct homotopy colimits and limits in an arbitrary model category. The key concept introduced is that of a model approximation. A model approximation of a category $\mathcal{C}$ with a given class of weak equivalences is a model category $\mathcal{M}$ together with a pair of adjoint functors $\mathcal{M} \rightleftarrows \mathcal{C}$ which satisfy certain properties. The key result says that if $\mathcal{C}$ admits a model approximation then so does the functor category $Fun(I, \mathcal{C})$.


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