Theory and Formal Methods 1993 pp 100-114 | Cite as

# Self-duality, Minimal Invariant Objects and Karoubi Invariance in Information Categories

## Abstract

We introduce IP-categories by enriching the notion of I-category (information category) such that every inclusion morphism has a right adjoint or projection. Categories of information systems for various domains in semantics are all examples of IP-categories. We show. that a weak notion of substructure relation between two Scott information systems induces general adjunctions between them. An IP-category with a zero object has the self-dual property that its opposite is again an IP-category. In a complete IP-category with a zero object, limits and colimits of chains of projections and inclusions coincide. As a consequence of the self-duality, a simple characterisation of minimal invariant objects of contravariant and mixed functors on IP-categories is obtained. IP-categories are closed under taking the Karoubi envelope. We use the arrow category of an effectively given IP-category to solve domain equations in categories of continuous information systems effectively.

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