Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On groupoids with involutions and their cohomology   We extend the definitions and main properties of graded extensions to the
category of locally compact groupoids endowed with involutions. We introduce
Real \v{C}ech cohomology, which is an equivariant-like cohomology theory
suitable for the context of groupoids with involutions. The Picard group of
such a groupoid is discussed and is given a cohomological picture. Eventually,
we generalize Crainic's result, about the differential cohomology of a proper
Lie groupoid with coefficients in a given representation, to the topological
case.

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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th