Une catéade, qu'est-ce que c'est?
Richard Garner – 18 January 2012, 25 January 2012
A catead in a finitely complete 2-category K is an internal category whose source-target span is a two-sided discrete fibration. Cateads were named and studied by Bourn and Penon in their preprint "2-Catégories réductibles" (now a TAC reprint).We show that cateads in the finitely complete K are precisely those internal categories whose externalisation (K_0)^op -> Cat extends to a 2-functor K^op -> Cat. We deduce that the 2-category Kat(K) of cateads, internal functors and internal natural transformations, is an exact completion of K: the closure of the representables in [K^op, Cat] under finite limits and codescent objects of cateads.