香蕉视频

Title: An Algebraic Combinatorial Approach to the Abstract Syntax of Opetopic Structures
Abstract
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 formalised in a categorical setting, unifying the algebraic aspects of the theory of abstract syntax [2, 3] and the theory of opetopes [6]. This realization allows one to transport viewpoints between the two 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 [1] for generating opetopes. The technical work will involve setting up a microcosm principle for near-semirings [5] and exploiting it in the cartesian closed bicategory of generalised species of structures [4].

(References may be found on the seminar webpage)