Warning 21.5.4. The terminology regarding final functors is extremey inconsistent in the literature. Because of historic reasons, final functors are also called cofinal functors, where the ‘co’ roughly means ‘jointly final’ and has nothing to do with the usual meaning of ‘co’ in category theory. Nevertheless, some authors use the words ‘final’ and ‘cofinal’ for the two notions from Definition 21.5.2, and there is no consensus as to which of the two words should refer to which of the two notions.
We hope that the convention in Definition 21.5.2 is easy to remember in light of the following lemma:
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