000177708 001__ 177708
000177708 005__ 20190316235407.0
000177708 02470 $$2ISI$$a000332041300008
000177708 0247_ $$2doi$$a10.1112/plms/pdt038
000177708 037__ $$aARTICLE
000177708 245__ $$aThe homotopy theory of coalgebras over a comonad
000177708 269__ $$a2014
000177708 260__ $$c2014
000177708 336__ $$aJournal Articles
000177708 520__ $$aLet 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.
000177708 6531_ $$aComonad
000177708 6531_ $$amodel category
000177708 6531_ $$acoring
000177708 700__ $$0240499$$aHess, Kathryn$$g105396
000177708 700__ $$aShipley, Brooke
000177708 773__ $$j108$$k2$$q484-516$$tProceedings of the London Mathematical Society
000177708 8564_ $$s358276$$uhttps://infoscience.epfl.ch/record/177708/files/Published.pdf$$yPostprint$$zPostprint
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000177708 937__ $$aEPFL-ARTICLE-177708
000177708 973__ $$aEPFL$$rREVIEWED$$sPUBLISHED
000177708 980__ $$aARTICLE