## Paper: Higher Dimensional Multigraphs (at LICS 1998)

**Claudio Hermida Michael Makkai A. John Power**

### Abstract

We introduce the notion of higher dimensional multigraph. This notion extends that of multigraph, which underlies multicategories and is essentially equivalent to the notion of context-free grammar. We develop the definition and explain how it gives a semantically coherent category theoretic approach to the notion of higher order context-free grammar. It also gives a conceptual framework in which one can study rewrites, and rewrites of rewrites, etcetera, for proofs of sequent calculus. The definition involves a subtle interaction between geometry and linearly defined syntax; we explore the latter here, outlining the geometric intuition

### BibTeX

@InProceedings{HermidaMakkaiPower-HigherDimensionalMu, author = {Claudio Hermida and Michael Makkai and A. John Power}, title = {Higher Dimensional Multigraphs}, booktitle = {Proceedings of the Thirteenth Annual IEEE Symposium on Logic in Computer Science (LICS 1998)}, year = {1998}, month = {June}, pages = {199--206}, location = {Indianapolis, IN, USA}, publisher = {IEEE Computer Society Press} }