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?



A Category-ish Structure with Morphism Domains containing Multiple Objects?
This structure is known as a multicategory. There are many references; e.g., see [Wikipedia](http://en.m.wikipedia.org/wiki/Multicategory) 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*](http://arxiv.org/pdf/math/0305049v1.pdf), by Leinster (see page 35). One nice introduction is also the [Catsters' video playlist](https://www.youtube.com/playlist?list=PLA2E14CCDF7A0EF91).


