Notes on 2-groupoids, 2-groups and crossed modules
نویسندگان
چکیده
منابع مشابه
Crossed squares, crossed modules over groupoids and cat$^{bf {1-2}}-$groupoids
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....
متن کاملbraiding from 2-groups to 2-groupoids
we give the concept of ‘braiding’ for 2-groupoids, and we show that this structure is equivalent tobraided regular, crossed modules.
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In this paper, we construct a neat description of the passage from crossed squares of commutative algebras to 2-crossed modules analogous to that given by Conduché in the group case. We also give an analogue, for commutative algebra, of T.Porter’s [13] simplicial groups to n-cubes of groups which implies an inverse functor to Conduché’s one.
متن کاملCrossed modules, pictures, and 2-dimensional topology
Two-dimensional cell complexes form a remarkably rich class of objects; indeed, one can regard all of group theory as a sub-theory of 2-dimensional topology. One of the key invariants at our disposal is the second homotopy group, π2, and starting with the work of Whitehead and Reidemeister, a good theory of the structure of π2 has been developed. The aim of the talk is to describe this basic st...
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ژورنال
عنوان ژورنال: Homology, Homotopy and Applications
سال: 2007
ISSN: 1532-0073,1532-0081
DOI: 10.4310/hha.2007.v9.n1.a3