Background
Basic concepts
equivalences in/of $(\infty,1)$-categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
The notion of locally small $(\infty,1)$-category is the generalization of the notion of locally small category from category theory to (∞,1)-category theory.
A quasi-category $C$ is locally small if for all objects $x,y \in C$ the hom ∞-groupoid $Hom_C(x,y)$ is essentially small.
This appears as HTT, below prop. 5.4.1.7.
A quasi-category $C$ is locally small precisely if the following equivalent condition holds:
for every small set $S$ of objects in $C$, the full sub-quasi-category on $S$ is essentially small.
This is the topic of section 5.4.1 of
Created on April 14, 2010 at 18:20:09. See the history of this page for a list of all contributions to it.