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University of Cambridge > Talks.cam > Logic and Semantics Seminar (Computer Laboratory) > An Algebraic Combinatorial Approach to the Abstract Syntax of Opetopic Structures

## An Algebraic Combinatorial Approach to the Abstract Syntax of Opetopic StructuresAdd to your list(s) Download to your calendar using vCal - Marcelo Fiore, University of Cambridge
- Friday 14 October 2016, 14:00-15:00
- FW26.
If you have a question about this talk, please contact Dominic Mulligan. The starting point of the talk will be the identification of structure common to tree-like combinatorial objects, exemplifying the situation with abstract syntax trees (as used in formal languages) and with opetopes (as used in higher-dimensional algebra). The emerging mathematical structure will be then formalized in a categorical setting, unifying the algebraic aspects of the theory of abstract syntax of [2, 3] and the theory of opetopes of [5]. This realization conceptually allows one to transport viewpoints between these, now bridged, mathematical theories and I will explore it here in the direction of higher-dimensional algebra, giving an algebraic combinatorial framework for a generalisation of the slice construction of [1] for generating opetopes. 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 [4]. Connections to (cartesian and symmetric monoidal) equational theories, lambda calculus, and algebraic combinatorics will be mentioned in passing. References - J.Baez and J.Dolan. Higher-Dimensional Algebra III . n-Categories and the Algebra of Opetopes. Advances in Mathematics 135, pages 145–206, 1998.
- 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.
- 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.
- 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.
- S.Szawiel and M.Zawadowski. The web monoid and opetopic sets. In arXiv:1011.2374 [math.CT], 2010.
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