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Interchanging homotopy limits and colimits in CAT

Guillermo Cortiñas
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Abstract

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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Guillermo Cortiñas. 2000-02-23. Interchanging homotopy limits and colimits in CAT. https://arxiv.org/abs/math/0001146

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