Abstract

Using the structure of a KZ-monad we create a general categorical workspace in which diagrams can be formally constructed. In particular this abstract framework of category theory is shown to provide a precise semantics for constructing the specifications of complex systems from their component parts. 1 Introduction The purely equational 2-dimensional categorical algebra underlying the process of freely completing categories under a given suitable class of colimits is presented by Kock in [8]. A common feature of the category which freely completes another category is that it has diagrams (functors) as its objects. Using properties of adjointness Kock identifies a particular monad which is called either a `monad with the Kock property' or a `KZ-doctrine'. Kock shows that this type of monad, which has structures which are adjoint to units, expresses precisely the properties of free cocompleteness and colimit formation in a category. In this paper the properties of a KZ-doctrine ar...

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