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pro vyhledávání: '"STEVENSON, DANNY"'
Autor:
Stevenson, Danny
We give a new construction of the Joyal model structure on the category of simplicial sets, and we provide a simple characterization of the fibrations in it. We characterize the inner anodyne maps in terms of categorical equivalences and use this cha
Externí odkaz:
http://arxiv.org/abs/1810.05233
Autor:
Stevenson, Danny
We study the notion of a bifibration in simplicial sets which generalizes the classical notion of two-sided discrete fibration studied in category theory. If $A$ and $B$ are simplicial sets we equip the category of simplicial sets over $A\times B$ wi
Externí odkaz:
http://arxiv.org/abs/1807.08226
Autor:
Stevenson, Danny
Publikováno v:
Theory and Application of Categories, Vol. 33, 2018, No. 19, pp. 523-536
In this paper we prove a stability result for inner fibrations in terms of the wide, or fat join operation on simplicial sets. We also prove some additional results on inner anodyne morphisms that may be of independent interest.
Comment: v4: pub
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Externí odkaz:
http://arxiv.org/abs/1608.07699
Autor:
Stevenson, Danny
Publikováno v:
North-West. Eur. J. Math. Vol. 3 (2017) pp. 141-202
In this paper we prove that for any simplicial set $B$, there is a Quillen equivalence between the covariant model structure on $\mathbf{S}/B$ and a certain localization of the projective model structure on the category of simplicial presheaves on th
Externí odkaz:
http://arxiv.org/abs/1512.04815
Publikováno v:
Advances in Theoretical and Mathematical Physics 21 (2017) no. 4 pp 921-975
We develop the theory of simplicial extensions for bundle gerbes and their characteristic classes with a view towards studying descent problems and equivariance for bundle gerbes. Equivariant bundle gerbes are important in the study of orbifold sigma
Externí odkaz:
http://arxiv.org/abs/1506.07931
Publikováno v:
Journal of Homotopy and Related Structures, Volume 10, Issue 3 (2015), pages 565-622
We discuss two aspects of the presentation of the theory of principal infinity-bundles in an infinity-topos, introduced in [NSSa], in terms of categories of simplicial (pre)sheaves. First we show that over a cohesive site C and for G a presheaf of si
Externí odkaz:
http://arxiv.org/abs/1207.0249
Publikováno v:
Journal of Homotopy and Related Structures, Volume 10, Issue 4 (2015), pages 749-801
The theory of principal bundles makes sense in any infinity-topos, such as that of topological, of smooth, or of otherwise geometric infinity-groupoids/infinity-stacks, and more generally in slices of these. It provides a natural geometric model for
Externí odkaz:
http://arxiv.org/abs/1207.0248
Autor:
Stevenson, Danny
In this paper we describe a classifying theory for families of simplicial topological groups. If $B$ is a topological space and $G$ is a simplicial topological group, then we can consider the non-abelian cohomology $H(B,G)$ of $B$ with coefficients i
Externí odkaz:
http://arxiv.org/abs/1203.2461
Publikováno v:
New York Journal of Mathematics Volume 22 (2016) 405-440
In this paper we study the classifying theory of principal bundles in the parametrized setting, motivated by recent interest in higher gauge theory. Using simplicial techniques, we construct a product-preserving classifying space functor for groups i
Externí odkaz:
http://arxiv.org/abs/1203.2460
Publikováno v:
Comm. Math. Phys. 319(2):379-393, 2013
In gauge theory, the Faddeev-Mickelsson-Shatashvili anomaly arises as a prolongation problem for the action of the gauge group on a bundle of projective Fock spaces. In this paper, we study this anomaly from the point of view of bundle gerbes and giv
Externí odkaz:
http://arxiv.org/abs/1112.1752