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32
Fibrations of groupoids
 J. Algebra
, 1970
"... theory, and change of base for groupoids and multiple ..."
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Cited by 41 (16 self)
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theory, and change of base for groupoids and multiple
Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional localtoglobal problems
 in Michiel Hazewinkel (ed.), Handbook of Algebra, volume 6, Elsevier
"... ..."
Computations and homotopical applications of induced crossed modules
 J. Symb. Comp
"... We explain how the computation of induced crossed modules allows the computation of certain homotopy 2types and, in particular, second homotopy groups. We discuss various issues involved in computing induced crossed modules and give some examples and applications. ..."
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Cited by 16 (8 self)
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We explain how the computation of induced crossed modules allows the computation of certain homotopy 2types and, in particular, second homotopy groups. We discuss various issues involved in computing induced crossed modules and give some examples and applications.
On the Schreier theory of nonabelian extensions: generalisations and computations
 Proc. Roy. Irish Acad. Sect. A
, 1996
"... We use presentations and identities among relations to give a generalisation of the Schreier theory of nonabelian extensions of groups. This replaces the usual multiplication table for the extension group by more efficient, and often geometric, data. The methods utilise crossed modules and crossed r ..."
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Cited by 13 (8 self)
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We use presentations and identities among relations to give a generalisation of the Schreier theory of nonabelian extensions of groups. This replaces the usual multiplication table for the extension group by more efficient, and often geometric, data. The methods utilise crossed modules and crossed resolutions.
Properties of Monoids That Are Presented By Finite Convergent StringRewriting Systems  a Survey
, 1997
"... In recent years a number of conditions has been established that a monoid must necessarily satisfy if it is to have a presentation through some finite convergent stringrewriting system. Here we give a survey on this development, explaining these necessary conditions in detail and describing the rela ..."
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Cited by 11 (5 self)
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In recent years a number of conditions has been established that a monoid must necessarily satisfy if it is to have a presentation through some finite convergent stringrewriting system. Here we give a survey on this development, explaining these necessary conditions in detail and describing the relationships between them. 1 Introduction Stringrewriting systems, also known as semiThue systems, have played a major role in the development of theoretical computer science. On the one hand, they give a calculus that is equivalent to that of the Turing machine (see, e.g., [Dav58]), and in this way they capture the notion of `effective computability' that is central to computer science. On the other hand, in the phrasestructure grammars introduced by N. Chomsky they are used as sets of productions, which form the essential part of these grammars [HoUl79]. In this way stringrewriting systems are at the very heart of formal language theory. Finally, they are also used in combinatorial semig...
Interpretations of Yetter's notion of Gcoloring: simplicial fibre bundles and nonabelian cohomology
, 1995
"... this article, but beware of misprints. A more thorough treatment is given in May, [18]. We will use (standard) notation from [18] wherever possible. The way found initially around the restriction that K had to be reduced in the above loop construction was to take a maximal tree in K and to contract ..."
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Cited by 11 (1 self)
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this article, but beware of misprints. A more thorough treatment is given in May, [18]. We will use (standard) notation from [18] wherever possible. The way found initially around the restriction that K had to be reduced in the above loop construction was to take a maximal tree in K and to contract it to a point. In 1984, a groupoid version of the loop group construction was given by Dwyer and Kan, [12]. (Unfortunately the published paper has many misprints and the cleanedup version that we will use was prepared by my student Phil Ehlers as part of his master's dissertation, [13]. Alternatives have been proposed by Joyal and Tierney, and by Moerdijk and Svensson. They end up with simplicial objects in the category of groupoids, whilst the Dwyer  Kan version gives a simplicially enriched groupoid, i.e. a groupoid all of whose Homobjects are simplicial sets. A simplicially enriched groupoid is also a simplicial groupoid (simplicial object in the category of groupoids), but is one whose object of objects is a constant simplicial set.) Let SS denote the category of simplicial sets and SGpds that of simplicially enriched groupoids or as we will often call them, simply, simplicial groupoids. The loop groupoid functor is a functor
Crossed complexes, and free crossed resolutions for amalgamated sums and HNNextensions of groups
 Georgian Math. J
, 1999
"... Dedicated to Hvedri Inassaridze for his 70th birthday The category of crossed complexes gives an algebraic model of CWcomplexes and cellular maps. Free crossed resolutions of groups contain information on a presentation of the group as well as higher homological information. We relate this to the p ..."
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Cited by 8 (7 self)
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Dedicated to Hvedri Inassaridze for his 70th birthday The category of crossed complexes gives an algebraic model of CWcomplexes and cellular maps. Free crossed resolutions of groups contain information on a presentation of the group as well as higher homological information. We relate this to the problem of calculating nonabelian extensions. We show how the strong properties of this category allow for the computation of free crossed resolutions for amalgamated sums and HNNextensions of groups, and so obtain computations of higher homotopical syzygies in these cases. 1
Homotopy Theory, and Change of Base for Groupoids and Multiple Groupoids
, 1996
"... This survey article shows how the notion of "change of base", used in some applications to homotopy theory of the fundamental groupoid, has surprising higher dimensional analogues, through the use of certain higher homotopy groupoids with values in forms of multiple groupoids. ..."
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Cited by 7 (6 self)
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This survey article shows how the notion of "change of base", used in some applications to homotopy theory of the fundamental groupoid, has surprising higher dimensional analogues, through the use of certain higher homotopy groupoids with values in forms of multiple groupoids.
Internal categorical structure in homotopical algebra
 Proceedings of the IMA workshop ?nCategories: Foundations and Applications?, June 2004, (to appear). CROSSED MODULES AND PEIFFER CONDITION 135 [Ped95] [Por87
, 1995
"... Abstract. This is a survey on the use of some internal higher categorical structures in algebraic topology and homotopy theory. After providing a general view of the area and its applications, we concentrate on the algebraic modelling of connected (n + 1)types through cat ngroups. 1. ..."
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Cited by 5 (3 self)
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Abstract. This is a survey on the use of some internal higher categorical structures in algebraic topology and homotopy theory. After providing a general view of the area and its applications, we concentrate on the algebraic modelling of connected (n + 1)types through cat ngroups. 1.
Formal Homotopy Quantum Field Theories, I: Formal Maps and . . .
, 2008
"... Homotopy Quantum Field Theories (HQFTs) were introduced by the second author to extend the ideas and methods of Topological Quantum Field Theories to closed dmanifolds endowed with extra structure in the form of homotopy classes of maps into a given ‘target ’ space. For d = 1, classifications of HQ ..."
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Cited by 5 (2 self)
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Homotopy Quantum Field Theories (HQFTs) were introduced by the second author to extend the ideas and methods of Topological Quantum Field Theories to closed dmanifolds endowed with extra structure in the form of homotopy classes of maps into a given ‘target ’ space. For d = 1, classifications of HQFTs in terms of algebraic structures are known when B is a K(G,1) and also when it is simply connected. Here we study general HQFTs with d = 1 and target a general 2type, giving a common generalisation of the classifying algebraic structures for the two cases previously known. The algebraic models for 2types that we use are crossed modules, C, and we introduce a notion of formal Cmap, which extends the usual latticetype constructions to this setting. This leads to a classification of ‘formal’ 2dimensional HQFTs with target C,