Abstract Marcelo Fiore

Algebraic structure common to type theory and higher-dimensional algebra

The starting point of this work is 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.  This involves setting up and exploiting a microcosm principle for near-semirings 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.

 

 

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