model category, model $\infty$-category
Definitions
Morphisms
Universal constructions
Refinements
Producing new model structures
Presentation of $(\infty,1)$-categories
Model structures
for $\infty$-groupoids
on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
for equivariant $\infty$-groupoids
for rational $\infty$-groupoids
for rational equivariant $\infty$-groupoids
for $n$-groupoids
for $\infty$-groups
for $\infty$-algebras
general $\infty$-algebras
specific $\infty$-algebras
for stable/spectrum objects
for $(\infty,1)$-categories
for stable $(\infty,1)$-categories
for $(\infty,1)$-operads
for $(n,r)$-categories
for $(\infty,1)$-sheaves / $\infty$-stacks
The classical model category structure on pointed topological spaces $Top^{\ast/}_{Quillen}$ is the model structure on pointed objects of the classical model structure on topological spaces $Top_{Quillen}$ under the point (a pointed model category).
Equipped 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.
Textbook accounts:
Last revised on July 20, 2021 at 10:34:56. See the history of this page for a list of all contributions to it.