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I labeled the equation.
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Lukas Woike
Lukas Woike
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For a finite group denote by $\mathbf{Ch}^G$ the dg-category of $G$-representations in chain complexes over a field.

Is there a tensor product $\otimes$ of dg-categories (similar to the Deligne tensor product for Abelian categories) such that for another finite group $H$ \begin{align} \mathbf{Ch}^{G\times H} \cong \mathbf{Ch}^G \otimes \mathbf{Ch}^H \quad \quad ?\end{align}\begin{align} (*) \quad \quad \mathbf{Ch}^{G\times H} \cong \mathbf{Ch}^G \otimes \mathbf{Ch}^H \quad \quad ?\end{align}

Thanks for any hints.

For a finite group denote by $\mathbf{Ch}^G$ the dg-category of $G$-representations in chain complexes over a field.

Is there a tensor product $\otimes$ of dg-categories (similar to the Deligne tensor product for Abelian categories) such that for another finite group $H$ \begin{align} \mathbf{Ch}^{G\times H} \cong \mathbf{Ch}^G \otimes \mathbf{Ch}^H \quad \quad ?\end{align}

Thanks for any hints.

For a finite group denote by $\mathbf{Ch}^G$ the dg-category of $G$-representations in chain complexes over a field.

Is there a tensor product $\otimes$ of dg-categories (similar to the Deligne tensor product for Abelian categories) such that for another finite group $H$ \begin{align} (*) \quad \quad \mathbf{Ch}^{G\times H} \cong \mathbf{Ch}^G \otimes \mathbf{Ch}^H \quad \quad ?\end{align}

Thanks for any hints.

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Lukas Woike
Lukas Woike
  • 1.4k
  • 7
  • 11

A tensor product for dg-categories

For a finite group denote by $\mathbf{Ch}^G$ the dg-category of $G$-representations in chain complexes over a field.

Is there a tensor product $\otimes$ of dg-categories (similar to the Deligne tensor product for Abelian categories) such that for another finite group $H$ \begin{align} \mathbf{Ch}^{G\times H} \cong \mathbf{Ch}^G \otimes \mathbf{Ch}^H \quad \quad ?\end{align}

Thanks for any hints.