177708
20190316235407.0
ISI
000332041300008
doi
10.1112/plms/pdt038
ARTICLE
The homotopy theory of coalgebras over a comonad
2014
2014
Journal Articles
Let K be a comonad on a model category M. We provide conditions under which the associated category of K-coalgebras admits a model category structure such that the forgetful functor to M creates both cofibrations and weak equivalences. We provide concrete examples that satisfy our conditions and are relevant in descent theory and in the theory of Hopf-Galois extensions. These examples are specific instances of the following categories of comodules over a coring. For any semihereditary commutative ring R, let A be a dg R-algebra that is homologically simply connected. Let V be an A-coring that is semifree as a left A-module on a degreewise R-free, homologically simply connected graded module of finite type. We show that there is a model category structure on the category of right A-modules satisfying the conditions of our existence theorem with respect to the comonad given by tensoring over A with V and conclude that the category of V-comodules in the category of right A-modules admits a model category structure of the desired type. Finally, under extra conditions on R, A, and V, we describe fibrant replacements in this category of comodules in terms of a generalized cobar construction.
Comonad
model category
coring
240499
Hess, Kathryn
105396
Shipley, Brooke
108
2
484-516
Proceedings of the London Mathematical Society
358276
http://infoscience.epfl.ch/record/177708/files/Published.pdf
Postprint
Postprint
252139
UPHESS
U10968
oai:infoscience.tind.io:177708
SV
article
GLOBAL_SET
105396
105396
105396
105396
148230
EPFL-ARTICLE-177708
EPFL
REVIEWED
PUBLISHED
ARTICLE