Received: from siufuxsun04.unifr.ch by UFPER6.UNIFR.CH via Pony Express SMTP with TCP (v8.1.1-dmr001); Mon, 3 Dec 1 16:25:33 MET Received: from localhost ([127.0.0.1] helo=siufuxsun03.unifr.ch) by siufuxsun04.unifr.ch with esmtp (Exim 3.22 #3) id 16AuyK-0007dt-00 for heinrich.kleisli@unifr.ch; Mon, 03 Dec 2001 16:25:32 +0100 Received: from mailserv.mta.ca ([138.73.101.5]) by siufuxsun03.unifr.ch with esmtp (Exim 3.22 #2) id 16AuyH-0004cM-00 for Heinrich.Kleisli@unifr.ch; Mon, 03 Dec 2001 16:25:29 +0100 Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16AuWW-0000sE-00 for categories-list@mta.ca; Mon, 03 Dec 2001 10:56:48 -0400 Message-Id: <5.1.0.14.1.20011130181434.009ef8d0@mailx.u-picardie.fr> X-Sender: ehres@mailx.u-picardie.fr X-Mailer: QUALCOMM Windows Eudora Version 5.1 Date: Sat, 01 Dec 2001 19:20:09 +0100 To: categories@mta.ca From: Andree Ehresmann <Andree.Ehresmann@u-picardie.fr> Subject: categories: Re: the walking adjunction and biadjunction Mime-Version: 1.0 Sender: cat-dist@mta.ca Precedence: bulk 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