Orbifolds and groupoids
نویسندگان
چکیده
منابع مشابه
Orbifolds, Sheaves and Groupoids
We characterize orbifolds in terms of their sheaves, and show that orbifolds correspond exactly to a specific class of smooth groupoids. As an application, we construct fibered products of orbifolds and prove a change-of-base formula for sheaf cohomology. Mathematics Subject Classifications (1991): 22A22, 57S15, 55N30, 18B25.
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The purpose of this paper is to describe orbifolds in terms of (a certain kind of) groupoids. In doing so, I hope to convince you that the theory of (Lie) groupoids provides a most convenient language for developing the foundations of the theory of orbifolds. Indeed, rather than defining all kinds of structures and invariants in a seemingly ad hoc way, often in terms of local charts, one can us...
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Abstract. We build a concrete and natural model for the strict 2-category of orbifolds. In particular we prove that if one localizes the 2-category of proper etale Lie groupoids at a class of 1-arrows that we call “covers,” then the strict 2-category structure drops down to the localization. In our construction the spaces of 1and 2-arrows admit natural topologies, the space of morphisms (1-arro...
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We discuss two generalizations of Lie groupoids. One consists of Lie n-groupoids defined as simplicial manifolds with trivial πk≥n+1. The other consists of stacky Lie groupoids G ⇒ M with G a differentiable stack. We build a 1–1 correspondence between Lie 2-groupoids and stacky Lie groupoids up to a certain Morita equivalence. We prove this in a general set-up so that the statement is valid in ...
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The aim of this paper is to introduce the notion of cat$^{bf {1}}-$groupoids which are the groupoid version of cat$^{bf {1}}-$groups and to prove the categorical equivalence between crossed modules over groupoids and cat$^{bf {1}}-$groupoids. In section 4 we introduce the notions of crossed squares over groupoids and of cat$^{bf {2}}-$groupoids, and then we show their categories are equivalent....
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2012
ISSN: 0166-8641
DOI: 10.1016/j.topol.2011.11.043