A new study entitled GRAPHS FOR JUNCTURE by Kosta Dosen and Zoran Petric (viii+128 pp.) is available at: http://www.mi.sanu.ac.rs/~kosta/jun.pdf _____________________________________ Abstract An alternative foundation for 2-categories is explored by studying graph-theoretically a partial operation on 2-cells named juncture, which can replace vertical and horizontal composition. Juncture is a generalized vertical composition of 2-cells that need not involve the whole target and the whole source; it may involve them only partially, provided the result is again a 2-cell. Since commuting diagrams of arrows of ordinary categories may be conceived as invertible 2-cells, this study concerns ordinary category theory too. The operation of juncture has a connection with proof theory, where it corresponds to a kind of cut rule on sequents, and it is related also to an operation on which the notion of operad can be based. The main achievement of the work is a detailed description of the specific planarity involved in juncture and graphs of 2-cells, comparable to the usual combinatorial characterizations of planarity in graph theory. ____________________________________ Subject Classification (MSC2010) Graph Theory: 05C10 (Planar graphs), 05C20 (Directed graphs), 05C62 (Graph representations), 05C76 (Graph operations) Category Theory: 18A10 (Graphs, diagram schemes), 18D05 (2-categories) ____________________________________ [For admin and other information see: http://www.mta.ca/~cat-dist/ ]