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
A model category structure on the category Operad of Set-enriched coloured symmetric operads which generalizes the canonical model structure on Cat.
Call a morphism of operads $f : P \to Q$ a weak equivalence if
its underlying functor of categories is an essentially surjective functor;
for every collection $(c_1, \cdots, c_n; c)$ of colours it induces an isomorphism
(the operadic analog of being full and faithful).
Call a morphism $f : P \to Q$ a fibration if for every isomorphism in $Q$ and a lift of its source object to $P$ there is an isomorphism in $P$ covering it under $f$.
Call a morphism a cofibration if it is an injection on objects (on colours)
This defines a cofibrantly generated model category structure on Operad.
This is due to (Weiss 07).
Last revised on February 29, 2012 at 01:56:50. See the history of this page for a list of all contributions to it.