On the "walking adjunction" I don't know the Pumplun's paper cited by Wyler. But there is another reference at about the same time; indeed, the "walking adjunction" has been explicitly constructed and studied in the paper of Auderset: "Adjonction et monade au niveau des 2-cat=E9gories" published in "Cahiers de Top. et Geom. Diff." XV-1 (1974), 3-20. More formally it could also be called "the 2-sketch of an adjunction" in the terminology in my paper with Charles Ehresmann: "Categories of sketched structures", in the "Cahiers" XIII-2 (1972), reprinted in "Charles Ehresmann: Oeuvres completes et commentees" Part IV-2. To add a remark on the terminology: When Charles introduced the concept of a sketch (already in a Kansas report of1966, cf. "Oeuvres" Parts III-2 and IV-1), the aim was to define the 'Platonist idea' of a structure, not only of a purely algebraic one, but also of structures like categories (partially defined operations), fields, or even topologies. He thought first of calling a sketch an idea, but then reserved the word "idea" for the smallest part which helps reconstruct the sketch; for instance for a category, the arrows which 'represent' the domain and codomain maps and the composition law. Sincerely Andree C. Ehresmann