nLab
Scott topos

Contents

Context

Category theory

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 Scott topos is a topos-theoretic generalization of the Scott topology on a domain.

Definition

The following definition is due to Karazeris (2001).

Definition

Let 𝒦\mathcal{K} be a finitely accessible category and 𝒦 f\mathcal{K}_f the full subcategory of its finitely presentable objects. The topos Set 𝒦 fSet^{\mathcal{K}_f} is called the Scott topos of 𝒦\mathcal{K} and denoted by σ𝒦\sigma\mathcal{K}.

Properties

Example

References

  • J. Adámek, A categorical generalization of Scott domains , Math. Struc. Comp. Sci. 7 pp.419-443.

  • P. Karazeris, Categorical Domain Theory: Scott Topology, Powercategories, Coherent Categories , TAC 9 (2001) pp.106-120. (abstract)

  • J. Velebil, Categorical Domain Theory , Diss. Prague 1998. (pdf)

  • J. Velebil, Categorical Generalization of a Universal Domain , Appl. Cat. Struc. 7 (1999) pp.209-226.

Last revised on March 13, 2018 at 12:05:17. See the history of this page for a list of all contributions to it.