essentially small (infinity,1)-category
objects such that commutes with certain colimits
The notion of essentially small -category is the generalization of the notion of essentially small category from category theory to (∞,1)-category theory.
This appears as HTT, def. 22.214.171.124, prop. 126.96.36.199.
In the presence of the regular extension axiom (which follows from the axiom of choice), essential smallness is equivalent to being essentially -small for some small regular cardinal .
This is HTT, prop. 188.8.131.52
The analogous statement holds for ∞-groupoids.
This is (HTT, corollary 184.108.40.206).
This is the topic of section 5.4.1 of
Revised on December 11, 2011 07:21:12
by Urs Schreiber