on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
The classical model category structure on pointed topological spaces $Top^{\ast/}_{Quillen}$ is the model structure on an undercategory of the classical model structure on topological spaces $Top_{Quillen}$ under the point (a pointed model category).
With the smash product this is a monoidal model category.
Recall that the generatic cofibrations of the classical model structure on topological spaces are
and the generating acylic cofibrations are
Write
for the operation of freely adjoining a basepoint.
The coslice model structure $(Top_{Quillen})^{\ast/}$ is itself cofibrantly generated, with generating cofibrations
and generating acyclic cofibrations
This is a special case of a general statement about cofibrant generation of coslice model structures, see this proposition.
Last revised on January 31, 2021 at 20:56:36. See the history of this page for a list of all contributions to it.