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Keywords:
controlled objects; symmetric monoidal functors; coarse algebraic $K$-homology theory
controlled objects; symmetric monoidal functors; coarse algebraic $K$-homology theory
Summary:
The goal of this paper is to associate functorially to every symmetric monoidal additive category $\bf A$ with a strict $G$-action a lax symmetric monoidal functor ${\bf V}^G_{\bf A}:G{\bf BornCoarse} \rightarrow {\bf Add}_\infty$ from the symmetric monoidal category of $G$-bornological coarse spaces $G{\bf BornCoarse}$ to the symmetric monoidal $\infty$-category of additive categories ${\bf Add}_\infty$. Among others, this allows to refine equivariant coarse algebraic $K$-homology to a lax symmetric monoidal functor.
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