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    • CommentRowNumber1.
    • CommentAuthorPeter Heinig
    • CommentTimeJul 25th 2017
    • (edited Jul 25th 2017)

    Changes-note. Changed the already existing page 201707051600 I created, to now contain another svg illustration, planned to be used in pasting schemes soon. Sort-of-a-permission for this is

    Power’s proof of (I guess you mean) his pasting theorem would probably be very handy to have discussed at the nLab. It would seem to fit at one of pasting diagram or pasting scheme, but less well at an article on some notion of graph I think. If you could even just write down the precise definitions of these various notions, that would also be very fine in my opinion.

    herein

    End of changes-note

    Metadata. What 201707051600 is: relevant material to create an nLab article on pasting schemes. More specifically: to document A. J. Power’s proof of one of the rigorous formalizations of the notational practice of pasting diagrams. 201707051600 shows a plane digraph GG. Vertex q q_{-\infty} is an \infty-coking in GG. Vertex q q_{\infty} is an \infty-king in GG. Connection to A 2-Categorical Pasting Theorem, Journal of Algebra 129 (1990): therein, the author calls q q_{-\infty} a “source”, and q q_{\infty} a “sink”. This is fine but not in tune with contemporary (digraph-theoretic) terminology, whereas “king” and “coking” are. These technical digraph-theoretic terms will be defined in digraph.

    Related concepts: pasting diagram, pasting scheme, digraph, planar graph, higher category theory.

    [ Some additional explanation: it was bad practice of me, partly excusable by the apparent LatestChanges-thread-starting-with-a-numeral-make-that-thread-invisible-forum-software-bug, to have created this page without notification and having it left unused for so long. Within reason, every illustration one publishes should be taken seriously, and documented. Much can be read on this of course, one useful reference for mathematicians is the TikZ&PGF manual, Version 3.0.0, Chapter 7, Guidelines on Graphics. My intentions were well-meant, in particular to improve the documentation of monoidal-enriched bicategories on the nLab. This is still work in progress, but to get the digraph/pasting scheme project under way is more urgent. Will re-use the 201707* named pages for this purpose, for tidiness. ]

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