Abstract

The significance of the 2-dimensional calculus, which goes back to Penrose, has already been pointed out by Joyal and Street in [JoS91]. Independently, Burroni has introduced a general notion of n-dimensional presentation in [Bur91] and he has shown that the equational logic of terms is a special case of 2-dimensional calculus. Here, we propose a combinatorial definition of 2-dimensional diagrams and a simple method for proving that certain monoidal categories are finitely 2-presentable. We illustrate the translation of terms into diagrams and we explain the change from groups to quantum groups in a purely syntactical way. This paper should serve as a reference for our future work on symbolic computation, including a theory of 2-dimensional rewriting and the design of software for interactive diagrammatic reasoning. New address: CNRS - Laboratoire de math'ematiques discr`etes, 163 avenue de Luminy - Case 930, 13288 Marseille Cedex 9, France. Email: lafont@lmd.univ-mrs.fr 2 1 FROM T...

Citations

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