Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopy Transition Cocycles   For locally homotopy trivial fibrations, one can define transition functions
$$ g\dab : U\da\cap U\db \to H = H(F)$$ where $H$ is the monoid of homotopy
equivalences of $F$ to itself but, instead of the cocycle condition, one
obtains only that $g\dab g\dbgam$ is homotopic to $g\dagam$ as a map of
$U\da\cap U\db\cap U\dgam$ into $H$. Moreover on multiple intersections, higher
homotopies arise and are relevant to classifying the fibration.
  The full theory was worked out by the first author in his 1965 Notre Dame
thesis \cite{wirth:diss}. Here we present it using language that has been
developed in the interim. We also show how this points a direction `on beyond
gerbes'.

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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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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: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga