An Algebraic Combinatorial Approach to Opetopic Structure

The starting point of this talk will be an algebraic connection to be  presented briefly between
the theory of abstract syntax of [1,2] and the approach to opetopic sets of [4].  This realization
conceptually allows us to transport viewpoints between these mathematical theories and I
will explore it here in the direction of higher-dimensional algebra leading to opetopic
categorical structures.  The technical work will involve setting up a microcosm principle
for near-semirings and subsequently exploiting it in the cartesian closed bicategory of
generalised species of structures [3].

References

[1] M.Fiore, G.Plotkin and D.Turi.  Abstract syntax and variable binding.
In 14th Logic in Computer Science Conf. (LICS'99), pages 193-202.  IEEE,
Computer Society Press, 1999.

[2] M.Fiore.  Second-order and dependently-sorted abstract syntax.  In
 Logic in Computer Science Conf. (LICS'08), pages 57-68.  IEEE, Computer
Society Press, 2008.

 [3] M.Fiore, N.Gambino, M.Hyland, and G.Winskel.  The cartesian closed
bicategory of generalised species of structures.  In J. London Math.
Soc., 77:203-220, 2008.

 [4] S.Szawiel and M.Zawadowski.  The web monoid and opetopic sets.  In
arXiv:1011.2374 [math.CT], 2010.