Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monomial $G$-posets and their Lefschetz invariants   Let $G$ be a finite group, and $C$ be an abelian group. We introduce the
notions of $C$-monomial $G$-sets and $C$-monomial $G$-posets, and state some of
their categorical properties. This gives in particular a new description of the
$C$-monomial Burnside ring $B_C(G)$. We also introduce Lefschetz invariants of
$C$-monomial $G$-posets, which are elements of $B_C(G)$. These invariants allow
for a definition of a generalized tensor induction multiplicative map
$\mathcal{T}_{U,\lambda}: B_C(G)\to B_C(H)$ associated to any $C$-monomial
$(G,H)$-biset $(U,\lambda)$, which in turn gives a group homomorphism
$B_C(G)^\times\to B_C(H)^\times$ between the unit groups of $C$-monomial
Burnside rings.

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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat