The Azimuth Project
Noncommutative Network Models

Idea

A construction is given for the free network model on a given monoid. Moreover, construct the free varietal network model on a monoid of a given variety?. To do this, give a generalization of the graph product of groups. Writing some classical combinatorial structures in categorical language is also involved.

References

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  • John Baez, John Foley?, Joseph Moeller, and Blake Pollard, Network Models, 2018. arXiv:1711.00037

  • S. N. Burris and H. P. Sankappanavar, A Course in Universal Algebra. Springer-Verlag, New York, (1981).

  • J. Fountain and M. Kambites, Graph products of right cancellative monoids. J. Aust. Math. Soc., 87(2):227–252, (2009).

  • E. R. Green, Graph products of groups. PhD thesis, University of Leeds, (1990).

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  • William Lawvere?, Functorial Semantics of Algebraic Theories? , Ph.D. thesis Columbia University (1963). Published with an author’s comment and a supplement in: Reprints in Theory and Applications of Categories 5 (2004) pp 1–121. (abstract)

  • William Lawvere?, Display of graphics and their applications, as exemplified by 2-categories and the hegelian “taco”. Proceedings of the First International Conference on Algebraic Methodology and Software Technology, University of Iowa, pages 51–74, (1989).

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  • A. Veloso da Costa. Graph products of monoids. Semigroup Forum, 63:247–277, (2001).