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
With braiding
With duals for objects
category with duals (list of them)
dualizable object (what they have)
ribbon category, a.k.a. tortile category
With duals for morphisms
monoidal dagger-category?
With traces
Closed structure
Special sorts of products
Semisimplicity
Morphisms
Internal monoids
Examples
Theorems
In higher category theory
A simplicial monoidal model category is a $sSet_{Qu}$-enriched monoidal model category, namely a model category equipped with
the structure of a monoidal model category,
the structure of a simplicial model category,
the compatibility structure that makes the underlying monoidal and sSet-enriched structure an
It ought to be true that the Bousfield localization at the “realization equivalences” (see this Prop.) of the Reedy model structure on simplicial objects in chain complexes is simplicial monoidal under the objectwise tensor product of chain complexes.
The notion may be implicit in many discussions of monoidal model category such as used, notably, to build symmetric monoidal smash products of spectra. One reference making more explicit the need to specify compatibility structure is:
with a precursor in
but the actual compatibility is maybe not made very explicit there either, for this see the references at enriched monoidal category.
Last revised on May 13, 2023 at 13:51:13. See the history of this page for a list of all contributions to it.