Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The convolution algebra of an absolutely locally compact topos   We introduce a class of toposes called "absolutely locally compact" toposes
and of "admissible" sheaf of rings over such toposes. To any such ringed topos
$(\mathcal{T},A)$ we attach an involutive convolution algebra
$\mathcal{C}_c(\mathcal{T},A)$ which is well defined up to Morita equivalence
and characterized by the fact that the category of non-degenerate modules over
$\mathcal{C}_c(\mathcal{T},A)$ is equivalent to the category of sheaf of
$A$-module over $\mathcal{T}$. In the case where $A$ is the sheaf of real or
complex Dedekind numbers, we construct several norms on this involutive algebra
that allows to complete it in various Banach and $C^*$-algebras:
$L^1(\mathcal{T},A)$, $C^*_{red}(\mathcal{T},A)$ and
$C^*_{max}(\mathcal{T},A)$. We also give some examples where this construction
corresponds to well known constructions of involutive algebras, like groupoids
convolution algebra and Leavitt path algebras.

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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio