Simplicial T-complexes and crossed complexes: a non-abelian version of a theorem of Dold and Kan

N. Ashley

GDML_Books, (1988), p.

Résumé

CONTENTSPreface (by Ronald Brown)..................................................................5Introduction..........................................................................................7Preliminaries........................................................................................91. T-complexes and crossed complexes.............................................101.1. A groupoid structure for a T-complex..........................................121.2. The isomorphism theorem for a T-complex.................................161.3. Certain abelian groups associated to a T-complex......................201.4. The homomorphism δ..................................................................221.5. The groupoid action....................................................................241.6. The interchange law between the isomorphisms h and φ............251.7. The crossed complex associated to a T-complex........................271.8. Some technical results................................................................311.9. The isomorphism theorem for T-complexes.................................331.10. The T-complex addition lemma..................................................351.11. A functor from crossed complexes to T-complexes....................361.12. The equivalence of categories..................................................402. Special filtered Kan complexes.......................................................412.1. Introduction.................................................................................412.2. Definitions and examples............................................................422.3. The crossed complex associated to the T-complex ϱ(X).............493. Simplicial groups............................................................................493.1. Group T-complexes.....................................................................503.2. Special simplicial groups over a groupoid...................................533.3. A filtration of a simplicial group....................................................544. Miscellaneous................................................................................54References........................................................................................58

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Zbl 1003.55500

EUDML-ID : urn:eudml:doc:268359