Interchanging homotopy limits and colimits in CAT

Details Interchanging homotopy limits and colimits in CAT Interchanging homotopy limits and colimits in CAT

2000-01-26

arxiv.org/abs/math/0001146v2

Boletin Acad. Nac. de Ciencias, 65, (2000) 95-102

Mathematics

Algebraic Topology

4 pages, AmsTex; typos corrected

Scientific paper

Let $I$,$J$ be small categories and $C:I\times J@>>>\CAT$ a functor to the
category of small categories. We show that if $I$ has a final object then the
canonical map
$\operatorname{hocolim}_J\operatorname{holim}_IC@>>>\operatorname{holim}_I
\operatorname{hocolim}_JC$ is a strong homotopy equivalence.

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