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
symmetric monoidal (∞,1)-category of spectra
An $E_\infty$-monoid (or E-infinity monoid object) in a symmetric monoidal model category $C$ is an algebra over an operad over the E-infinity operad. Assuming that $C$ is cofibrantly generated, there is a model structure on $E_\infty$-monoids, given by the model structure on algebras over an operad over the E-infinity operad (which is cofibrant). This model category presents the (infinity,1)-category of commutative monoids in a symmetric monoidal (infinity,1)-category (in the symmetric monoidal (infinity,1)-category presented by $C$).
In some symmetric monoidal model categories, $E_\infty$-monoids can be rectified to (strictly) commutative monoids in a symmetric monoidal model category. See there for more.
Created on March 11, 2015 at 13:15:32. See the history of this page for a list of all contributions to it.