Wreath Product of Set-Valued Functors and Tensor Multiplication |
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Authors: | Valdis Laan |
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Institution: | (1) Institute of Pure Mathematics, University of Tartu, 50409 Tartu, Estonia |
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Abstract: | Considering the wreath product functor $G wr H:{\cal A} wr^G{\cal B} \rightarrow \SET$ of functors $G: {\cal A}\rightarrow \SET$ and
$H: {\cal B}\rightarrow \SET$ over small categories $ {\cal A}$ and $ {\cal B}$, we prove that if tensor multiplication by the functor $G\wrr H$ preserves $ {\cal D}$-limits, where ${\cal D}$ is a small category, then tensor multiplication by $G$ preserves ${\cal D}$-limits, and if tensor multiplication by the functor $G wr H$ preserves ${\cal D}$-limits of representables then tensor multiplications by $G$ and $H$ preserve $ {\cal D}$-limits of representables. We also study flatness and pullback flatness of the wreath product of set-valued functors. |
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