Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stacky Buildings   We introduce structures which model quotients of buildings by type-preserving
group actions. These structures, which we call W-groupoids for W a Coxeter
group, generalize Bruhat decompositions, chambers systems of type M, Tits
amalgams, and buildings themselves. We define the fundamental group of a
W-groupoid, and characterize buildings as connected simply connected
W-groupoids. We give a brief outline of covering theory of W-groupoids, which
produces buildings as universal covers equipped with an action of the
fundamental group. The local-to-global theorem of Tits concerning spherical
3-resides allows for the construction of W-groupoids by amalgamating quotients
of generalized polygons along groupoids. In this way, W-groupoids provide a
powerful way to construct (lattices in) exotic, hyperbolic, and wild buildings.

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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an