I am working on formalizing software design using category theory.

However the most natural way for me to express what I want is with a Category where multiple morphisms can join into a single morphism.

Thinking diagrammatically, what I am talking about is multiple arrows (from different objects) merging into a single arrow before reaching an object. Kinda like an inverse arrow split.

Please note that I am not talking about Categories where objects can be (say) concatenations of multiple types. It also does not make sense (for what I am working on) to use currying.

So my question is: has this type of structure been researched? If yes what would be a good reference?


This structure is known as a multicategory. There are many references; e.g., see Wikipedia for a basic introduction, and read the nlab's page http://ncatlab.org:8080/nlab/show/multicategory as well. One very nice reference is the book Higher Operads, Higher Categories, by Leinster (see page 35). One nice introduction is also the Catsters' video playlist.

  • $\begingroup$ Perfect! Exactly what I was looking for. Thanks! $\endgroup$ – mbrodersen Dec 15 '14 at 6:03

The difficulty of composing with a multiset of multiarrows is that (unless the multiset of domains is actually a set), there will in general be more than one way to do that composition.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.