The formal ball model for -categories-Reference-Cited by-同舟云学术

The formal ball model for -categories

Published:2010-12-02 Issue:1 Volume:21 Page:41-64
ISSN:0960-1295
Container-title:Mathematical Structures in Computer Science
language:en
Short-container-title:Math. Struct. Comp. Sci.

Author:

KOSTANEK MATEUSZ,WASZKIEWICZ PAWEŁ

Abstract

We generalise the construction of the formal ball model for metric spaces due to A. Edalat and R. Heckmann in order to obtain computational models for separated

-categories. We fully describe

-categories that are

(a)Yoneda complete

(b)continuous Yoneda complete

via their formal ball models. Our results yield solutions to two open problems in the theory of quasi-metric spaces by showing that:

(a)a quasi-metric spaceXis Yoneda complete if and only if its formal ball model is a dcpo, and

(b)a quasi-metric spaceXis continuous and Yoneda complete if and only if its formal ball modelBXis a domain that admits a simple characterisation of approximation.

Publisher

Cambridge University Press (CUP)

Subject

Computer Science Applications,Mathematics (miscellaneous)

Reference41 articles.

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4. The limit–colimit coincidence theorem for -categories

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