It appears that the definition of 2-category was introduced independently by two authors, both of whom independently introduced the modern notion of enriched category, for which 2-categories appeared as an example. - Jean Bénabou gives 2-categories as example (5) in the 1965 paper [Catégories relatives](https://gallica.bnf.fr/ark:/12148/bpt6k4019v/f37.item), under the name "2-catégories". - Jean-Marie Maranda gives 2-categories as an example on the second page (p. 759) in the 1965 paper [Formal categories](https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/formal-categories/A7C463460EB8CAC64C2CA340F870CF80), under the name "categories of the second type". The definition is spelled out in §2. Both authors mention the connection to Ehresmann's double categories. --- Bénabou cites his own forthcoming thesis for the concept, which was eventually published under [Structures algébriques dans les catégories](http://www.numdam.org/item/?id=CTGDC_1968__10_1_1_0) (which is not precisely the name mentioned in the paper). He also points the reader to Ehresmann's 1963 [Catégories structurées](https://eudml.org/doc/urn:eudml:doc:81794), but the definition of 2-category does not appear here; the reference is most likely due to the similar notion of double category, of which the notion of 2-category is a special case. Other authors, such as Eilenberg and Kelly in the 1965 paper [Closed categories](https://link.springer.com/chapter/10.1007/978-3-642-99902-4_22), also cite Ehresmann's 1963 paper for the notion of 2-category. However, as it does not appear there, it is more likely they intended to cite Ehresmann's similarly named 1965 book *Catégories et structures* (which is the reference currently [listed on Wikipedia](https://en.wikipedia.org/wiki/Strict_2-category)), which does contain a discussion of 2-categories on page 324 in a historical note. To settle the matter, I emailed Andrée Ehresmann, who wrote: > [Charles Ehresmann] did not introduced himself 2-catégories, which have been introduced soon after both by his student Jean Bénabou as special double categories, and by different other authors as categories 'enriched' in Cat --- The appearance in SGA 4 of 2-categories appears to have either been introduced during editing, or was based on word-of-mouth ideas. SGA 4, for instance, cites Monique Hakim's 1972 thesis, who introduced 2-categories by writing: > La notion de 2-categorie est due a J. Benabou