Some Fundamental Algebraic Tools for the Semantics of Computation Part 3. Indexed Categories
R Burstall, J Goguen and A TarleckiAbstract: This paper presents indexed categories, which model uniformly defined families of categories, and suggests that they are a useful tool for the working computer scientist. An indexed category gives rise to a single flattened category as a disjoint union of its component categories plus some additional morphisms. Similarly, an indexed functor (which is a uniform family of functors between the component categories) induces a flattened functor between the corresponding flattened categories. Under certain assumptions, flattened categories are (co)complete if all their components are, and flattened functors have left adjoints if all their components do. Several examples are given.
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