TY - EJOUR
DO - 10.1112/plms/pdt038
AB - 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.
T1 - The homotopy theory of coalgebras over a comonad
IS - 2
DA - 2014
AU - Hess, Kathryn
AU - Shipley, Brooke
JF - Proceedings of the London Mathematical Society
SP - 484-516
VL - 108
EP - 484-516
ID - 177708
KW - Comonad
KW - model category
KW - coring
UR - http://infoscience.epfl.ch/record/177708/files/Published.pdf
ER -