Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Alternative Presentation of the Symmetric-Simplicial Category   The category Fin of symmetric-simplicial operators is obtained by enlarging
the category Ord of monotonic functions between the sets {0,1,...,n} to include
all functions between the same sets. Marco Grandis has given a presentation of
Fin using the standard generators Ord (cofaces and codegeneracies) as well as
the adjacent transpositions which generate the permutations in Fin. The purpose
of this note is to establish an alternative presentation of Fin in which the
codegeneracies are replaced by special maps which we call quasi-codegeneracies.
We also prove a unique factorization theorem for products of cofaces and
quasi-codegeneracies analogous to the standard unique factorizations in Ord.
This presentation has been used by the author to construct symmetric
hypercrossed complexes (to be published elsewhere) which are algebraic models
for homotopy types of spaces based on the hypercrossed complexes of Carrasco
and Cegarra.

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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph