Geodesic
Integral chains and Bousfield–Kan completion
Homology, homotopy, and applications, Tome 21 (2019) no. 2, pp. 29-58.

Voir la notice de l'article provenant de la source International Press of Boston

Working in the Arone–Ching framework for homotopical descent, it follows that the Bousfield–Kan completion map with respect to integral homology is the unit of a derived adjunction. We prove that this derived adjunction, comparing spaces with coalgebra complexes over the associated integral homology comonad, via integral chains, can be turned into a derived equivalence by replacing spaces with the full subcategory of simply connected spaces. In particular, this provides an integral chains characterization of the homotopy type of simply connected spaces.
DOI : 10.4310/HHA.2019.v21.n2.a4
Classification : 55N10, 55P60, 55P99
Keywords: completion, homotopical descent, coalgebra, integral chains 
@article{HHA_2019_21_2_a3,
     author = {Jacobson R. Blomquist and John E. Harper},
     title = {Integral chains and {Bousfield{\textendash}Kan} completion},
     journal = {Homology, homotopy, and applications},
     pages = {29--58},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2019},
     doi = {10.4310/HHA.2019.v21.n2.a4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2019.v21.n2.a4/}
}
TY  - JOUR
AU  - Jacobson R. Blomquist
AU  - John E. Harper
TI  - Integral chains and Bousfield–Kan completion
JO  - Homology, homotopy, and applications
PY  - 2019
SP  - 29
EP  - 58
VL  - 21
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4310/HHA.2019.v21.n2.a4/
DO  - 10.4310/HHA.2019.v21.n2.a4
LA  - en
ID  - HHA_2019_21_2_a3
ER  - 
%0 Journal Article
%A Jacobson R. Blomquist
%A John E. Harper
%T Integral chains and Bousfield–Kan completion
%J Homology, homotopy, and applications
%D 2019
%P 29-58
%V 21
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4310/HHA.2019.v21.n2.a4/
%R 10.4310/HHA.2019.v21.n2.a4
%G en
%F HHA_2019_21_2_a3
Jacobson R. Blomquist; John E. Harper. Integral chains and Bousfield–Kan completion. Homology, homotopy, and applications, Tome 21 (2019) no. 2, pp. 29-58. doi : 10.4310/HHA.2019.v21.n2.a4. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2019.v21.n2.a4/

Cité par Sources :