Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Twisted Version of the Classifying Space Functor   It is known that there is a weak-equivalence between the geometric
realization of a simplicially enriched small category and its cofibrant
replacement [12]. In this paper, we show that when only small categories are
considered there exists a homeomorphism between these geometric realizations.
We also discuss the naturality of these homoemorphisms. The inclusion of the
category of small categories to the category of simplicially enriched
categories, the cofibrant replacement of simplicially enriched categories, and
the geometric realization of simplicially enriched categories are three
composable functors. Hence one can ask if the collection of all these
homeomorphisms gives a natural transformation from the composition of these
three functors to the classifying space functor. We show that this is almost
the case and that this composition can be considered as some twisted version of
the classifying space functor. \end{abstract}

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The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
1
The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph