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Tensor products and homotopies for ωgroupoids and crossed complexes
, 2007
"... Crossed complexes have longstanding uses, explicit and implicit, in homotopy theory and the cohomology of groups. It is here shown that the category of crossed complexes over groupoids has a symmetric monoidal closed structure in which the internal Hom functor is built from morphisms of crossed comp ..."
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Cited by 54 (23 self)
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Crossed complexes have longstanding uses, explicit and implicit, in homotopy theory and the cohomology of groups. It is here shown that the category of crossed complexes over groupoids has a symmetric monoidal closed structure in which the internal Hom functor is built from morphisms of crossed complexes, nonabelian chain homotopies between them and similar higher homotopies. The tensor product involves nonabelian constructions related to the commutator calculus and the homotopy addition lemma. This monoidal closed structure is derived from that on the equivalent category of ωgroupoids where the underlying cubical structure gives geometrically natural definitions of tensor products and homotopies.
Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional localtoglobal problems
 in Michiel Hazewinkel (ed.), Handbook of Algebra, volume 6, Elsevier
"... ..."
Computing homotopy types using crossed ncubes of groups
 in Adams Memorial Symposium on Algebraic Topology
, 1992
"... Dedicated to the memory of Frank Adams ..."
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
Crossed complexes, free crossed resolutions and graph products of groups’, (submitted
"... 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 ..."
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Cited by 1 (1 self)
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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 of graph products of groups, and so obtain computations of higher homotopical syzygies in this case. 1