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Ensuring Software Quality in Information Systems

The work described here identifies facilities within category theory for guaranteeing quality in information systems. For relatively static aspects, the internal structure of the topos is explored further with particular emphasis on the nature of the pasted pullback, including the conditions for a pasting to be valid and the inherent recursive nature of pullback structures. For dynamic aspects, a banking example is explored, leading to the nature of the external processes acting upon the topos such as transactions. These processes are represented by monads, giving a three-level closure on the activity. The nature of monads is explored. The T-algebra enables changes to be made in the monad structure, giving the potential for adaptability. Monads, that have been strengthened by the Kleisli lift to the Cartesian form, can be composed naturally, facilitating the construction of quality large-scale information systems with the reliability required for transactions in the banking world.