Groupoids and crossed objects in algebraic topology
نویسندگان
چکیده
منابع مشابه
Groupoids and crossed objects in algebraic topology
This is an introductory survey of the passage from groups to groupoids and their higher dimensional versions, with most emphasis on calculations with crossed modules and the construction and use of homotopy double groupoids.
متن کاملNonabelian Algebraic Topology : filtered spaces , crossed complexes , cubical higher homotopy groupoids
متن کامل
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....
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This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...
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ژورنال
عنوان ژورنال: Homology, Homotopy and Applications
سال: 1999
ISSN: 1532-0073,1532-0081
DOI: 10.4310/hha.1999.v1.n1.a1