Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The global dimension of the algebra of the monoid of all partial
  functions on an $n$-set as the algebra of the EI-category of epimorphisms
  between subsets   We prove that the global dimension of the complex algebra of the monoid of
all partial functions on an n-set is $n-1$ for all $n\geq 1$. This is also the
global dimension of the complex algebra of the category of all epimorphisms
between subsets of an $n$-set. In our proof we use standard homological methods
as well as combinatorial techniques associated to the representation theory of
the symmetric group. As part of the proof, we obtain a partial description of
the Cartan matrix of these algebras.

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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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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: solv-int
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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: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg