Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cyclic homology for bornological coarse spaces   We define Hochschild and cyclic homologies for bornological coarse spaces:
for a fixed field $k$ and group $G$, these are lax symmetric monoidal functors
$\mathcal{X}HH_{k}^G$ and $\mathcal{X}HC_{k}^G$ from the category of
equivariant bornological coarse spaces $G\mathbf{BornCoarse}$ to the cocomplete
stable $\infty$-category of chain complexes $\mathbf{Ch}_\infty$. We relate
these equivariant coarse homology theories to coarse algebraic $K$-theory
$\mathcal{X} K^G_{k}$ and to coarse ordinary homology $\mathcal{X} H^G$ by
constructing a trace-like natural transformation $\mathcal{X} K_{k}^G\to
\mathcal{X} H^G$ that factors through coarse Hochschild (or cyclic) homology.
We further compare the forget-control map for coarse Hochschild homology with
the associated generalized assembly map.

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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio