nLab
(infinity,1)-semitopos

Definition

Definition

An (∞,1)-category $C$ is an $(\mathrm{\infty },1)$-semitopos if

1. it is presentable (∞,1)-category;

2. it has universal colimits;

3. for every morphism the corresponding Cech nerve groupoid object is effective.

This appears as HTT, def. 6.2.3.1.

Properties

Proposition

If $C$ is an $(\mathrm{\infty },1)$-semitopos and $X\in C$ is any object, then also the over-(∞,1)-category is an $(\mathrm{\infty },1)$-semitopos.

This appears as (HTT, remark 6.2.3.3).

Examples

• Of course every (∞,1)-topos is an $(\mathrm{\infty },1)$-semitopos.

Related concepts

• semitopos?

• (∞,1)-topos