Abstract
We show how the completeness and cocompleteness of the total category of a fibration can be inferred from that of the fibre categories and its base. Our results are somewhat stronger than those in [BGT91] and they are obtained as direct consequences of an important property of general fibred adjunctions. Our aim is to show that fibred category theory can provide insight into constructions of relevance in algebraic specifications, e.g. limits and colimits of many-sorted algebras, by explaining them at a natural level of abstraction.
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Hermida, C. (1994). On fibred adjunctions and completeness for fibred categories. In: Ehrig, H., Orejas, F. (eds) Recent Trends in Data Type Specification. ADT COMPASS 1992 1992. Lecture Notes in Computer Science, vol 785. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57867-6_14
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DOI: https://doi.org/10.1007/3-540-57867-6_14
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