Abstract
S is already built [Jay95]using a categorical pullback to capture the decomposition.The mere existence of the decomposition may sometimes be of use. For example,graph types are fundamental, but typically hidden by encodings, e.g. assparse arrays, when they should be manipulated directly, by both the programmerand the compiler. Another example arises when communicating a valuealong a channel. By sending the shape first, the receiver can fix the data structure,including pointers, etc.,...

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