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45
On algebraic models for homotopy 3types
 J. Homotopy Relat. Struct
"... We explore the relations among quadratic modules, 2crossed modules, crossed squares and simplicial groups with Moore complex of length 2. ..."
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We explore the relations among quadratic modules, 2crossed modules, crossed squares and simplicial groups with Moore complex of length 2.
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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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.
Freeness Conditions for Crossed Squares and Squared Complexes.
, 2008
"... Following Ellis, [9], we investigate the notion of totally free crossed square and related squared complexes. It is shown how to interpret the information in a free simplicial group given with a choice of CWbasis, interms of the data for a totally free crossed square. Results of Ellis then apply to ..."
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Following Ellis, [9], we investigate the notion of totally free crossed square and related squared complexes. It is shown how to interpret the information in a free simplicial group given with a choice of CWbasis, interms of the data for a totally free crossed square. Results of Ellis then apply to give a description in terms of tensor products of crossed modules. The paper ends with a purely algebraic derivation of a result
DoldKan Type Theorem for ΓGroups
, 1998
"... Introduction \Gammaspaces were introduced by Segal [S], who proved that they are combinatorial models for connective spectra (see also [A], [BF]). Based on KanThurston theorem we show that any \Gammaspace is stably weak equivalent to a discrete \Gammagroup. By a wellknown theorem of DoldKan th ..."
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Introduction \Gammaspaces were introduced by Segal [S], who proved that they are combinatorial models for connective spectra (see also [A], [BF]). Based on KanThurston theorem we show that any \Gammaspace is stably weak equivalent to a discrete \Gammagroup. By a wellknown theorem of DoldKan the Moore normalization establishes the equivalence between the category of simplicial abelian groups and the category of chain complexes (see [DP]). mimicking the construction of normalization of simplicial groups, we give a similar construction for \Gammagroups. This construction is based on the notion of crosseffects of functors [BP], which is a generalizatin of the classical definition of Eilenberg and Mac Lane [EM] to the nonabelian setup. Finally a DoldKan type theorem for the category of \Gammagroups is proved. In abelian case our theorem claims that the category of abelian \Gammagroups is equivalent to the category of functors Ab\Omega , where\Om
Calculus of functors and model categories ii
 A CLASSIFICATION OF SMALL LINEAR FUNCTORS
, 2013
"... ar ..."
ON REALIZING DIAGRAMS OF ΠALGEBRAS
, 2006
"... Abstract. Given a diagram of Πalgebras (graded groups equipped with an action of the primary homotopy operations), we ask whether it can be realized as the homotopy groups of a diagram of spaces. The answer given here is in the form of an obstruction theory, of somewhat wider application, formulate ..."
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Abstract. Given a diagram of Πalgebras (graded groups equipped with an action of the primary homotopy operations), we ask whether it can be realized as the homotopy groups of a diagram of spaces. The answer given here is in the form of an obstruction theory, of somewhat wider application, formulated in terms of generalized Πalgebras. This extends a program begun in [DKS1, BDG] to study the realization of a single Πalgebra. In particular, we explicitly analyze the simple case of a single map, and provide a detailed example, illustrating the connections to higher homotopy operations. A recurring problem in algebraic topology is the rectification of homotopycommutative diagrams: given a diagram F: D → ho T ∗ (i.e., a functor from a small category to the homotopy category of topological spaces), we ask whether F lifts to ˆ F: D → T∗, and if so, in how many ways.