nLab Scott topos

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 $\sigma\mathcal{K}$.

Properties

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Example

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Related entries

• Scott topology

• domain theory

• accessible category

• exponentiable topos

• Dana Scott

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.