nLab
topos of pointed objects

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

The category of pointed objects 1\1\backslash \mathcal{E} of a topos \mathcal{E} has zero objects hence can be the degenerate topos at best. By altering the notion of morphism it is nevertheless possible to obtain a topos ^\bullet\mathcal{E} with objects 1X1\to X, called the topos of pointed objects.

Definition

Let \mathcal{E} be a topos. The topos ^\bullet\mathcal{E} of pointed objects has objects the morphisms 1X1\to X and morphisms pullback squares:

1 X 1 Y \begin{array}{cccc}1& \to & X \\ \downarrow & & \downarrow \\ 1 & \to & Y \end{array}

Properties

  • Foremost, ^\bullet\mathcal{E} is a topos (cf. Freyd 1987).

Reference

  • Peter Freyd, Choice and Well-ordering , APAL 35 (1987) pp.149-166. (section 5)

Last revised on February 15, 2020 at 12:12:44. See the history of this page for a list of all contributions to it.