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The formal ball model for -categories

Published online by Cambridge University Press:  02 December 2010

MATEUSZ KOSTANEK  and
PAWEŁ WASZKIEWICZ
MATEUSZ KOSTANEK
Affiliation:
Theoretical Computer Science, Jagiellonian University, ul. S. Łojasiewicza 6, 30-348 Kraków, Poland Email: [email protected].
PAWEŁ WASZKIEWICZ
Affiliation:
Theoretical Computer Science, Jagiellonian University, ul. S. Łojasiewicza 6, 30-348 Kraków, Poland Email: [email protected].
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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

  1. (a) Yoneda complete

  2. (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:

  1. (a) a quasi-metric space X is Yoneda complete if and only if its formal ball model is a dcpo, and

  2. (b) a quasi-metric space X is continuous and Yoneda complete if and only if its formal ball model BX is a domain that admits a simple characterisation of approximation.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 21 , Issue 1 , February 2011 , pp. 41 - 64
Copyright
Copyright © Cambridge University Press 2010

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