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

N. Ashley. Simplicial T-complexes and crossed complexes: a non-abelian version of a theorem of Dold and Kan. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1988. <http://eudml.org/doc/268359>.

@book{N1988,
abstract = {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},
author = {N. Ashley},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Simplicial T-complexes and crossed complexes: a non-abelian version of a theorem of Dold and Kan},
url = {http://eudml.org/doc/268359},
year = {1988},
}

TY - BOOK
AU - N. Ashley
TI - Simplicial T-complexes and crossed complexes: a non-abelian version of a theorem of Dold and Kan
PY - 1988
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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
LA - eng
UR - http://eudml.org/doc/268359
ER -