Polygraph

A polygraph signature, $𝓖$, is given by a set of objects, ${𝓖}_{\mathrm{obj}}$, and a set of polyedges $𝓖(X_1,...,X_n;Y_1,...,Y_m)$ for every two lists of objects $X_1,...,X_n\in {𝓖}_{\mathrm{obj}}$.

There are two notions of polyquiver morphism: rigid polyquiver morphism and expanding polyquiver morphism. These correspond to the category of sets and the Kleisli category of the list monad, respectively.

Notes.

• underlying polyquiver of a monoidal category
• unit of the polyquiver-monoidal adjunction
  • polycategory: a polyquiver induces a free polycategory

See also.

• distributive quiver
• Linear polyquiver

References

• The Geometry of Tensor Calculus I (Joyal, Street), Definition 1.4 (called tensor scheme).

Tags: signature, strict monoidal category.

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