Abstract
The significance of the 2-dimensional calculus, which goes back to Penrose, has already been pointed out by Joyal and Street. Independently, Burroni has introduced a general notion of n-dimensional presentation 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. In particular, we consider Burroni's presentation of finite maps and we extend it to the case of finite relations.
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.
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© 1995 Springer-Verlag Berlin Heidelberg
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Lafont, Y. (1995). Equational reasoning with 2-dimensional diagrams. In: Comon, H., Jounnaud, JP. (eds) Term Rewriting. TCS School 1993. Lecture Notes in Computer Science, vol 909. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59340-3_13
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DOI: https://doi.org/10.1007/3-540-59340-3_13
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