nLab
locally small (infinity,1)-category

Contents

Idea

The notion of locally small (,1)(\infty,1)-category is the generalization of the notion of locally small category from category theory to (∞,1)-category theory.

Definitions

Definition

A quasi-category CC is locally small if for all objects x,yCx,y \in C the hom ∞-groupoid Hom C(x,y)Hom_C(x,y) is essentially small.

This appears as HTT, below prop. 5.4.1.7.

Properties

Proposition

A quasi-category CC is locally small precisely if the following equivalent condition holds:

for every small set SS of objects in CC, the full sub-quasi-category on SS is essentially small.

References

This is the topic of section 5.4.1 of

Created on April 14, 2010 18:48:38 by Urs Schreiber (131.211.232.49)