nLab (infinity,1)-semitopos

Context

$(\infty,1)$-Category theory

(∞,1)-category theory

Models

$(\infty,1)$-Topos Theory

(∞,1)-topos theory

Constructions

structures in a cohesive (∞,1)-topos

Contents

Definition

Definition

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

1. it has universal colimits;

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

This appears as (HTT, remark 6.2.3.3).

Examples

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

Created on November 4, 2011 15:01:05 by Urs Schreiber (82.113.121.180)