nLab
model structure for weak complicial sets
Contents
Context
Higher category theory
higher category theory
Basic concepts
Basic theorems
Applications
Models
Morphisms
Functors
Universal constructions
Extra properties and structure
1-categorical presentations
Model category theory
model category
Definitions
Morphisms
Universal constructions
Refinements
Producing new model structures
Presentation of $(\infty,1)$-categories
Model structures
for $\infty$-groupoids
for ∞-groupoids
for $n$-groupoids
for $\infty$-groups
for $\infty$-algebras
general
specific
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
Contents
Idea
The notion of weak complicial set is a model for (the omega-nerve of) the notion of weak ∞-category. The model structure for weak $\omega$-categories is a model category structure on the category of stratified simplicial sets, such that cofibrant-fibrant objects are precisely the weak complicial sets. This model structure may therefore be understood as a presentation of the (∞,1)-category of weak $\omega$-categories.
References
Section 6 of
Last revised on November 10, 2014 at 20:41:13.
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