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This is a generalization of a multicategory like https://gist.github.com/plt-amy/174cf949e4cad7a24c1c73d0cdc6c35b However, I didn't require isArity to be a proposition so that the finite ordinals also qualify as arities. This is a generalization of both non-symmetric and symmetric multicategories, and it also allows multicategories with infinite-arity morphisms. I am currently not sure of the relation to Tom Leinster's generalized multicategories.

anshwad10 added 5 commits May 28, 2025 17:26
This is a generalization of a multicategory like https://gist.github.com/plt-amy/174cf949e4cad7a24c1c73d0cdc6c35b
However, I didn't require isArity to be a proposition so that isFinOrd also qualifies as an arity.
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I'll add more when the next version of cubical is supported and the error is fixed

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I am currently not sure of the relation to Tom Leinster's generalized multicategories.

I think Tom Leinster's multicategories are actually more general than these: Given some S : ArityType there is a (wild) monad M on Type defined by M X = Σ[ I ∈ Arity ] ⟨ I ⟩ → X; isArity-⊤ provides the unit, isArity-Σ gives the join, and isArity-idl isArity-idr isArity-assoc give the monad laws. An S-multicategory in this sense is precisely a M-multicategory in their sense
So I'm going to try again with a more general definition parameterized by an arbritrary wild monad

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