I am curious to know how all this fits with partial algebraic operations. The axioms for a groupoid allow for the empty groupoid. That reminds me that Philip Higgins wrote about partial algebraic structures in @article {Higgins-algebrawithoperators, AUTHOR = {Higgins, Philip J.}, TITLE = {Algebras with a scheme of operators}, JOURNAL = {Math. Nachr.}, FJOURNAL = {Mathematische Nachrichten}, VOLUME = {27}, YEAR = {1963}, PAGES = {115--132}, ISSN = {0025-584X}, MRCLASS = {18.10}, MRNUMBER = {MR0163940 (29 \#1239)}, MRREVIEWER = {A. Heller}, } and he told me that years later he got a paper from a computer scientist saying `Higgins' theorem is true as stated' , which apparently concerned the empty structure! Does anyone on this list know a reference for axioms for group theory which are related to Dakin's axioms for a simplicial T-complex; 1) degenerate implies thin; 2) every horn has a unique thin filler; 3) if all faces but one of a thin element are thin, then so also is the remaining face. The last axiom is related to associativity. I am sure I had a reference at one time, but have lost it. Ronnie Brown burroni@math.jussieu.fr wrote:
Hi, You can find this equation (and ref to Higman and Neumann) in the GTM springer no 26 page 7 : E.G. manes "Algebraic Theory. xxxdydzdxxdxdzddd=y (polish notations and d is the binary operation.)
Best, Albert
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]