nLab
(infinity,1)-semitopos

Context

(,1)(\infty,1)-Category theory

(,1)(\infty,1)-Topos Theory

(∞,1)-topos theory

Background

Definitions

Characterization

Morphisms

Extra stuff, structure and property

Models

Constructions

structures in a cohesive (∞,1)-topos

Contents

Definition

Definition

An (∞,1)-category CC is an (,1)(\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 CC is an (,1)(\infty,1)-semitopos and XCX \in C is any object, then also the over-(∞,1)-category is an (,1)(\infty,1)-semitopos.

This appears as (HTT, remark 6.2.3.3).

Examples

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

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