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The reason why I did not add this to compiler_hints is that currently the information only makes sense for a given tower. E.g. the total number of morphisms needed to construct a FreydCategory morphism depends of course on the underlying category. If we compile a tower without wrapping it, there is no natural place to store this information, expect the call to PrecompileCategory.
In the future it would be nice if a category could specify how many underlying objects and morphisms are used to create an object or morphism, and CompilerForCAP could collect this information for any given tower. But for now, this is a very primitive system.
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