topos theory

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 $C$ with a terminal object $*$ such that

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

2. for every covering family $\{f_i : U_i \to U\}$ in $C$ the morphism

$\coprod_i Hom_C(*,f_i) : \coprod_i Hom_C(*, U_i) \to Hom_C(*, U)$

is surjective.

Examples

Revised on May 24, 2016 13:46:43 by Anonymous Coward (128.62.21.208)