nLab concrete site

Contents

Context

Topos Theory

topos theory

Background

Toposes

Internal Logic

Topos morphisms

Extra stuff, structure, properties

Cohomology and homotopy

In higher category theory

Theorems

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

    is surjective.

Examples

Last revised on May 24, 2016 at 17:46:43. See the history of this page for a list of all contributions to it.