13,361 research outputs found
n-Groupoids and Stacky Groupoids
We discuss two generalizations of Lie groupoids. One consists of Lie
-groupoids defined as simplicial manifolds with trivial .
The other consists of stacky Lie groupoids \cG\rra M with \cG 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 both differential and
topological categories. \Equivalences of higher groupoids in various categories
are also described.Comment: 45 pages, include other categories than a previous paper--
arXiv:math/0609420 [math.DG], edited version, typos removed, more details on
axioms of stacky groupoids. to appear in IMR
SMARANDACHE GROUPOIDS
In this paper we study the concept of Smarandache Groupoids, subgroupoids,
ideal of groupoids, semi-normal subgroupoids, Smarandache-Bol groupoids and
Strong Bol groupoids and obtain many interesting results about them
Integration of Dirac-Jacobi structures
We study precontact groupoids whose infinitesimal counterparts are
Dirac-Jacobi structures. These geometric objects generalize contact groupoids.
We also explain the relationship between precontact groupoids and homogeneous
presymplectic groupoids. Finally, we present some examples of precontact
groupoids.Comment: 10 pages. Brief changes in the introduction. References update
The snail lemma for internal groupoids
We establish a generalized form both of the Gabriel-Zisman exact sequence associated with a pointed functor between pointed groupoids, and of the Brown exact sequence associated with a fibration of pointed groupoids. Our generalization consists in replacing pointed groupoids with groupoids internal to a pointed regular category with reflexive coequalizer
On twisted contact groupoids and on integration of twisted Jacobi manifolds
We introduce the concept of twisted contact groupoids, as an extension either
of contact groupoids or of twisted symplectic ones, and we discuss the
integration of twisted Jacobi manifolds by twisted contact groupoids. We also
investigate the very close relationships which link homogeneous twisted Poisson
manifolds with twisted Jacobi manifolds and homogeneous twisted symplectic
groupoids with twisted contact ones. Some examples for each structure are
presented
2-Vector Spaces and Groupoids
This paper describes a relationship between essentially finite groupoids and
2-vector spaces. In particular, we show to construct 2-vector spaces of
Vect-valued presheaves on such groupoids. We define 2-linear maps corresponding
to functors between groupoids in both a covariant and contravariant way, which
are ambidextrous adjoints. This is used to construct a representation--a weak
functor--from Span(Gpd) (the bicategory of groupoids and spans of groupoids)
into 2Vect. In this paper we prove this and give the construction in detail.Comment: 44 pages, 5 figures - v2 adds new theorem, significant changes to
proofs, new sectio
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