On weak higher dimensional categories. I: Part 1
This is the first part of a three-part paper introducing the concept of multitopic set, which is intended as a foundation for a construction of weak higher-dimensional categories. Multitopic sets are analogous to the opetopic sets of \textit{J. C. Baez} and \textit{J. Dolan} [``Higher-dimensional algebra. III: \(n\)-categories and the algebra of opetopes'', Adv. Math. 135, No. 2, 145-206 (1998; Zbl 0909.18006)], but they are more geometric. A multitopic set consists of cells and pasting diagrams in various dimensions, where the pasting diagrams are got from the cells by amalgamation, using ideas from multicategory theory. Cells and pasting diagrams of dimension \(k\) have domains and codomains of dimension \(k-1\); the domains are arbitrary pasting diagrams but the codomains are cells. This first part of the paper consists of an informal introduction; details will be given in later parts.
scientific article; zbMATH DE number 1538807