Crossed modules as homotopy normal maps
نویسندگان
چکیده
منابع مشابه
Crossed Modules as Homotopy Normal Maps
In this note we consider crossed modules of groups (N → G, G→ Aut(N)), as a homotopy version of the inclusion N ⊂ G of a normal subgroup. Our main observation is a characterization of the underlying map N → G of a crossed module, in terms of a simplicial group structure on the associated bar construction. This approach allows for “natural” generalizations to other monoidal categories, in partic...
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We obtain some explicit calculations of crossed Q modules induced from a crossed module over a normal subgroup P of Q By virtue of theorems of Brown and Higgins this enables the computation of the homotopy types and second homotopy modules of certain homotopy pushouts of maps of classifying spaces of discrete groups Introduction A crossed module M M P has a classifying space BM see for example ...
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We obtain some explicit calculations of crossedQ-modules induced from a crossed module over a normal subgroup P of Q. By virtue of theorems of Brown and Higgins, this enables the computation of the homotopy 2-types and second homotopy modules of certain homotopy pushouts of maps of classifying spaces of discrete groups. Introduction A crossed module M = (μ : M → P ) has a classifying space BM (...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2010
ISSN: 0166-8641
DOI: 10.1016/j.topol.2009.09.004