Contents

category theory

topos theory

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

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 16:05:17. See the history of this page for a list of all contributions to it.