Homotopy Theory of Diagrams

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  • Homotopy Theory of Diagrams Book Detail

  • Author : Wojciech Chachólski
  • Release Date : 2002
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 106
  • ISBN 13 : 0821827596
  • File Size : 43,43 MB

Homotopy Theory of Diagrams by Wojciech Chachólski PDF Summary

Book Description: 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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