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Higherdimensional algebra and topological quantum field theory
 Jour. Math. Phys
, 1995
"... For a copy with the handdrawn figures please email ..."
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Cited by 140 (14 self)
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For a copy with the handdrawn figures please email
From groups to groupoids: a brief survey
 Bull. London Math. Soc
, 1987
"... A groupoid should be thought of as a group with many objects, or with many identities. A precise definition is given below. A groupoid with one object is essentially just a group. So the notion of groupoid is an extension of that of groups. It gives an additional convenience, flexibility and range o ..."
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Cited by 59 (7 self)
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A groupoid should be thought of as a group with many objects, or with many identities. A precise definition is given below. A groupoid with one object is essentially just a group. So the notion of groupoid is an extension of that of groups. It gives an additional convenience, flexibility and range of applications, so that even for purely grouptheoretical work, it can be useful to take a path through the world of groupoids.
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 (2 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
Double categories, 2categories . . .
 THEORY APPL. CATEG
, 1999
"... The main result is that two possible structures which may be imposed on an edge symmetric double category, namely a connection pair and a thin structure, are equivalent. A full proof is also given of the theorem of Spencer, that the category of small 2categories is equivalent to the category of edg ..."
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The main result is that two possible structures which may be imposed on an edge symmetric double category, namely a connection pair and a thin structure, are equivalent. A full proof is also given of the theorem of Spencer, that the category of small 2categories is equivalent to the category of edge symmetric double categories with thin structure.
Some Problems In NonAbelian Homotopical And Homological Algebra
, 1999
"... this paper is to convey some impression of the extent of an area of nonAbelian homotopical and homological algebra, by giving some of the problems, of varying degrees of diculty and of precision, which I have come across over the years and in which progress would be desirable. ..."
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this paper is to convey some impression of the extent of an area of nonAbelian homotopical and homological algebra, by giving some of the problems, of varying degrees of diculty and of precision, which I have come across over the years and in which progress would be desirable.