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1.
The simplicial interpretation of bigroupoid 2torsors
Open Access
Title:
The simplicial interpretation of bigroupoid 2torsors
Author:
Igor Baković
Igor Baković
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Description:
Actions of bicategories arise as categorification of actions of categories. They appear in a variety of different contexts in mathematics, from Moerdijk’s classification of regular Lie groupoids in foliation theory [34] to Waldmann’s work on deformation quantization [38]. For any such action we introduce an action bicategory, together with a can...
Actions of bicategories arise as categorification of actions of categories. They appear in a variety of different contexts in mathematics, from Moerdijk’s classification of regular Lie groupoids in foliation theory [34] to Waldmann’s work on deformation quantization [38]. For any such action we introduce an action bicategory, together with a canonical projection (strict) 2functor to the bicategory which acts. When the bicategory is a bigroupoid, we can impose the additional condition that action is principal in bicategorical sense, giving rise to a bigroupoid 2torsor. In that case, the Duskin nerve of the canonical projection is precisely the DuskinGlenn simplicial 2torsor, introduced in [25]. 1
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The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20121126
Source:
http://arxiv.org/pdf/0902.3436v1.pdf
http://arxiv.org/pdf/0902.3436v1.pdf
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text
Language:
en
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.247.4534
http://arxiv.org/pdf/0902.3436v1.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.247.4534
http://arxiv.org/pdf/0902.3436v1.pdf
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2.
Bigroupoid 2tensors
Open Access
Title:
Bigroupoid 2tensors
Author:
Igor Baković
Igor Baković
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The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20120327
Source:
http://www.irb.hr/korisnici/ibakovic/2torsbig.pdf
http://www.irb.hr/korisnici/ibakovic/2torsbig.pdf
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en
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.210.2223
http://www.irb.hr/korisnici/ibakovic/2torsbig.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.210.2223
http://www.irb.hr/korisnici/ibakovic/2torsbig.pdf
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3.
In der vorliegenden Doktorarbeit werden zwei fundamentale Konzepte der höher dimensionalen
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Title:
In der vorliegenden Doktorarbeit werden zwei fundamentale Konzepte der höher dimensionalen
Author:
Igor Baković
Igor Baković
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Algebra, die Kategorifizierung und Internalisierung, verfolgt. Von der geometrischen
Algebra, die Kategorifizierung und Internalisierung, verfolgt. Von der geometrischen
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The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20120625
Source:
http://edoc.ub.unimuenchen.de/9209/1/Bakovic_Igor.pdf
http://edoc.ub.unimuenchen.de/9209/1/Bakovic_Igor.pdf
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text
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en
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.233.5407
http://edoc.ub.unimuenchen.de/9209/1/Bakovic_Igor.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.233.5407
http://edoc.ub.unimuenchen.de/9209/1/Bakovic_Igor.pdf
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4.
The classifying topos of a topological bicategory
Open Access
Title:
The classifying topos of a topological bicategory
Author:
Igor Baković
Igor Baković
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For any topological bicategory 2C, the Duskin nerve N2C of 2C is a simplicial space. We introduce the classifying topos B2C of 2C as the Deligne topos of sheaves Sh(N2C) on the simplicial space N2C. It is shown that the category of topos morphisms Hom(Sh(X), BC) from the topos of sheaves Sh(X) on a topological space X to the Deligne classifying ...
For any topological bicategory 2C, the Duskin nerve N2C of 2C is a simplicial space. We introduce the classifying topos B2C of 2C as the Deligne topos of sheaves Sh(N2C) on the simplicial space N2C. It is shown that the category of topos morphisms Hom(Sh(X), BC) from the topos of sheaves Sh(X) on a topological space X to the Deligne classifying topos is naturally equivalent to the category of principal Cbundles. As a simple consequence, the geometric realization N2C  of the nerve N2C of a locally contractible topological bicategory 2C is the classifying space of principal 2Cbundles (on CW complexes), giving a variant of the result of Baas, Bökstedt and Kro derived in the context of bicategorical Ktheory [1]. We also define classifying topoi of a topological bicategory 2C using sheaves on other types of nerves of a bicategory given by Lack and Paoli [13], Simpson [17] and Tamsamani [18] by means of bisimplicial spaces, and we examine their properties. 1
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The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20121126
Source:
http://arxiv.org/pdf/0902.1750v1.pdf
http://arxiv.org/pdf/0902.1750v1.pdf
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Document Type:
text
Language:
en
DDC:
514 Topology
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.247.9529
http://arxiv.org/pdf/0902.1750v1.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.247.9529
http://arxiv.org/pdf/0902.1750v1.pdf
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5.
The classifying topos of a topological bicategory
Open Access
Title:
The classifying topos of a topological bicategory
Author:
Igor Baković
Igor Baković
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Description:
For any topological bicategory 2C, the Duskin nerve N2C of 2C is a simplicial space. We introduce the classifying topos B2C of 2C as the Deligne topos of sheaves Sh(N2C) on the simplicial space N2C. It is shown that the category of topos morphisms Hom(Sh(X), BC) from the topos of sheaves Sh(X) on a topological space X to the Deligne classifying ...
For any topological bicategory 2C, the Duskin nerve N2C of 2C is a simplicial space. We introduce the classifying topos B2C of 2C as the Deligne topos of sheaves Sh(N2C) on the simplicial space N2C. It is shown that the category of topos morphisms Hom(Sh(X), BC) from the topos of sheaves Sh(X) on a topological space X to the Deligne classifying topos is naturally equivalent to the category of principal Cbundles. As a simple consequence, the geometric realization N2C  of the nerve N2C of a locally contractible topological bicategory 2C is the classifying space of principal 2Cbundles (on CW complexes), giving a variant of the result of Baas, Bökstedt and Kro derived in the context of bicategorical Ktheory [1]. We also define classifying topoi of a topological bicategory 2C using sheaves on other types of nerves of a bicategory given by Lack and Paoli [13], Simpson [17] and Tamsamani [18] by means of bisimplicial spaces, and we examine their properties. 1
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20121126
Source:
http://arxiv.org/pdf/0902.1750v2.pdf
http://arxiv.org/pdf/0902.1750v2.pdf
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Document Type:
text
Language:
en
DDC:
514 Topology
(computed)
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Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.247.3293
http://arxiv.org/pdf/0902.1750v2.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.247.3293
http://arxiv.org/pdf/0902.1750v2.pdf
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6.
Noncommutative gerbes and deformation quantization
Open Access
Title:
Noncommutative gerbes and deformation quantization
Author:
Paolo Aschieri
;
Igor Baković
;
Branislav Jurčo
Paolo Aschieri
;
Igor Baković
;
Branislav Jurčo
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Description:
We define noncommutative gerbes using the language of star products. Quantized twisted Poisson structures are discussed as an explicit realization in the sense of deformation quantization. Our motivation is the noncommutative description of
We define noncommutative gerbes using the language of star products. Quantized twisted Poisson structures are discussed as an explicit realization in the sense of deformation quantization. Our motivation is the noncommutative description of
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20130715
Source:
http://arxiv.org/pdf/hepth/0206101v1.pdf
http://arxiv.org/pdf/hepth/0206101v1.pdf
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Document Type:
text
Language:
en
Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.266.3874
http://arxiv.org/pdf/hepth/0206101v1.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.266.3874
http://arxiv.org/pdf/hepth/0206101v1.pdf
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7.
The simplicial interpretation of bigroupoid 2torsors
Open Access
Title:
The simplicial interpretation of bigroupoid 2torsors
Author:
Bakovic, Igor
Bakovic, Igor
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Description:
Actions of bicategories arise as categorification of actions of categories. They appear in a variety of different contexts in mathematics, from Moerdijk's classification of regular Lie groupoids in foliation theory, to Waldmann's work on deformation quantization. For any such action we introduce an action bicategory, together with a canonical pr...
Actions of bicategories arise as categorification of actions of categories. They appear in a variety of different contexts in mathematics, from Moerdijk's classification of regular Lie groupoids in foliation theory, to Waldmann's work on deformation quantization. For any such action we introduce an action bicategory, together with a canonical projection (strict) 2functor to the bicategory which acts. When the bicategory is a bigroupoid, we can impose the additional condition that action is principal in bicategorical sense, giving rise to a bigroupoid 2torsor. In that case, the Duskin nerve of the canonical projection is precisely the DuskinGlenn simplicial 2torsor. ; Comment: preliminary version
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Year of Publication:
20090219
Document Type:
text
Subjects:
Mathematics  Category Theory ; Mathematics  Algebraic Topology
Mathematics  Category Theory ; Mathematics  Algebraic Topology
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URL:
http://arxiv.org/abs/0902.3436
http://arxiv.org/abs/0902.3436
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8.
Bigroupoid 2torsors
Title:
Bigroupoid 2torsors
Author:
Baković, Igor
Baković, Igor
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Description:
"In this thesis we follow two fundamental concepts from the {\it higher dimensional algebra}, the {\it categorification} and the {\it internalization}. From the geometric point of view, so far the most general torsors were defined in the dimension $n=1$, by {\it actions of categories and groupoids}. In the dimension $n=2$, Mauri and Tierney, and...
"In this thesis we follow two fundamental concepts from the {\it higher dimensional algebra}, the {\it categorification} and the {\it internalization}. From the geometric point of view, so far the most general torsors were defined in the dimension $n=1$, by {\it actions of categories and groupoids}. In the dimension $n=2$, Mauri and Tierney, and more recently Baez and Bartels from the different point of view, defined less general 2torsors with the structure 2group. Using the language of simplicial algebra, Duskin and Glenn defined actions and torsors internal to any Barr exact category $\E$, in an arbitrary dimension $n$. This actions are simplicial maps which are {\it exact fibrations} in dimensions $m \geq n$, over special simplicial objects called {\it ndimensional Kan hypergroupoids}. The correspondence between the geometric and the algebraic theory in the dimension $n=1$ is given by the Grothendieck nerve construction, since the Grothendieck nerve of a groupoid is precisely a 1dimensional Kan hypergroupoid. One of the main results is that groupoid actions and groupoid torsors become simplicial actions and simplicial torsors over the corresponding 1dimensional Kan hypergroupoids, after the application of the Grothendieck nerve functor. The main result of the thesis is a generalization of this correspondence to the dimension $n=2$. This result is achieved by introducing two new algebraic and geometric concepts, {\it actions of bicategories} and {\it bigroupoid 2torsors}, as a categorification and an internalization of actions of categories and groupoid torsors. We provide the classification of bigroupoid 2torsors by {\it the second nonabelian cohomology} with coefficients in the structure bigroupoid. The second nonabelian cohomology is defined by means of the third new concept in the thesis, a {\it small 2fibration} corresponding to an internal bigroupoid in the category $\E$. The correspondence between the geometric and the algebraic theory in the dimension $n=2$ is given by the Duskin nerve construction for bicategories and bigroupoids since the Duskin nerve of a bigroupoid is precisely a 2dimensional Kan hypergroupoid. Finally, the main results of the thesis is that bigroupoid actions and bigroupoid 2torsors become simplicial actions and simplicial 2torsors over the corresponding 2dimensional Kan hypergroupoids, after the application of the Duskin nerve functor."
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Publisher:
LudwigMaximiliansUniversität München
Year of Publication:
20080627
Document Type:
Dissertation ; NonPeerReviewed
Subjects:
Fakultät für Mathematik ; Informatik und Statistik
Fakultät für Mathematik ; Informatik und Statistik
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DDC:
514 Topology
(computed)
Relations:
http://edoc.ub.unimuenchen.de/9209/
URL:
http://edoc.ub.unimuenchen.de/9209/1/Bakovic_Igor.pdf
http://nbnresolving.de/urn:nbn:de:bvb:1992092
http://edoc.ub.unimuenchen.de/9209/1/Bakovic_Igor.pdf
http://nbnresolving.de/urn:nbn:de:bvb:1992092
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University of Munich: Digital theses
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9.
The classifying topos of a topological bicategory
Open Access
Title:
The classifying topos of a topological bicategory
Author:
Bakovic, Igor
;
Jurco, Branislav
Bakovic, Igor
;
Jurco, Branislav
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Description:
For any topological bicategory B, the Duskin nerve NB of B is a simplicial space. We introduce the classifying topos BB of B as the Deligne topos of sheaves Sh(NB) on the simplicial space NB. It is shown that the category of geometric morphisms Hom(Sh(X),BB) from the topos of sheaves Sh(X) on a topological space X to the Deligne classifying topo...
For any topological bicategory B, the Duskin nerve NB of B is a simplicial space. We introduce the classifying topos BB of B as the Deligne topos of sheaves Sh(NB) on the simplicial space NB. It is shown that the category of geometric morphisms Hom(Sh(X),BB) from the topos of sheaves Sh(X) on a topological space X to the Deligne classifying topos is naturally equivalent to the category of principal Bbundles. As a simple consequence, the geometric realization NB of the nerve NB of a locally contractible topological bicategory B is the classifying space of principal Bbundles, giving a variant of the result of Baas, Bokstedt and Kro derived in the context of bicategorical Ktheory. We also define classifying topoi of a topological bicategory B using sheaves on other types of nerves of a bicategory given by Lack and Paoli, Simpson and Tamsamani by means of bisimplicial spaces, and we examine their properties. ; Comment: accepted for a publication in "Homology, Homotopy and Applications"
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Year of Publication:
20090210
Document Type:
text
Subjects:
Mathematics  Category Theory ; Mathematics  Algebraic Topology ; 18D05 ; 18B25 ; 55Fxx
Mathematics  Category Theory ; Mathematics  Algebraic Topology ; 18D05 ; 18B25 ; 55Fxx
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DDC:
514 Topology
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URL:
http://arxiv.org/abs/0902.1750
http://arxiv.org/abs/0902.1750
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10.
The classifying topos of a topological bicategory
Title:
The classifying topos of a topological bicategory
Author:
Jurčo, Branislav
;
Baković, Igor
Jurčo, Branislav
;
Baković, Igor
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Year of Publication:
2010
Source:
Homology, Homotopy and Applications, v.12, 279300 (2010)
Homology, Homotopy and Applications, v.12, 279300 (2010)
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Document Type:
Article
Language:
en
URL:
http://edoc.mpg.de/522691
http://edoc.mpg.de/522691
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Max Planck Society eDoc Server
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