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

  • Abbas Edalat
Conference paper
Part of the Workshops in Computing book series (WORKSHOPS COMP.)


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.


Information Category Domain Equation Invariant Object Projection Morphism General Adjunction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© British Computer Society 1993

Authors and Affiliations

  • Abbas Edalat
    • 1
  1. 1.Department of ComputingImperial CollegeLondonUK

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