On completeness of locally-internal categories
This paper will certainly be considered as a very interesting one by those people who believe that the theory of enriched categories is an elegant tool for explaining things in mathematics... but it will probably not be appreciated by some of those people who consider fibered categories as a more intuitive notion. In any case I did appreciate this paper very much. The basic idea is to view a category which is fibered over SETS as a category enriched in the bicategory of spans of sets. For enriched categories, there is an obvious extension of the classical notions of limit or completeness: when the fibered category is viewed as indicated, this gives precisely the apparently more sophisticated notion of completeness for fibrations. All those results are in fact proved in a much more general context, where SETS is replaced by an arbitrary topos.
scientific article; zbMATH DE number 4025659