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Homotopy colimits in the category of small categories

Published online by Cambridge University Press:  24 October 2008

R. W. Thomason
R. W. Thomason
Affiliation:
Massachusetts Institute of Technology
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Extract

In (13), Quillen defines a higher algebraic K-theory by taking homotopy groups of the classifying spaces of certain categories. Certain questions in K-theory then become questions such as when do functors induce a homotopy equivalence of classifying spaces, or when is a square of categories homotopy cartesian? Quillen has given some techniques for answering such questions. F. Waldhausen has extended these ideas in (19), and broadened the range of applications to include geometric topology (20).

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 85 , Issue 1 , January 1979 , pp. 91 - 109
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

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