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# Polygraph (mathematics)

In mathematics, and particularly in category theory, a polygraph is a generalisation of a directed graph. It is also known as a computad. They were introduced as "polygraphs" by Albert Burroni[1] and as "computads" by Ross Street.[2]

In the same way that a directed multigraph can freely generate a category, an n-computad is the "most general" structure which can generate a free n-category.[3]

References

A. Burroni. Higher-dimensional word problems with applications to equational logic. TCS, 115(1):43--62, 1993.

R. Street. Limits indexed by category-valued 2-functors. Journal of Pure and Applied Algebra, 8(2):149--181, 1976.

computad in nLab

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