nLab
concrete site

Context

Topos Theory

Could not include topos theory - contents

Contents

Idea

A concrete site is a site whose objects can be thought of as sets with extra structure: it is a category that is a concrete category and a site in a compatible way.

In a category of presheaves on a concrete site one can consider concrete presheaves.

Definition

Definition

A concrete site is a site CC with a terminal object ** such that

  1. the functor Hom C(*,):CSetHom_C(*,-) : C \to Set is a faithful functor;

  2. for every covering family {f i:U iU}\{f_i : U_i \to U\} in CC the morphism

    iHom C(*,f): iHom C(*,U i)Hom C(*,U) \coprod_i Hom_C(*,f) : \coprod_i Hom_C(*, U_i) \to Hom_C(*, U)

    is surjective.

Examples

Revised on October 15, 2010 08:05:28 by Urs Schreiber (87.212.203.135)