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$C$-monoids and their variants is what you are looking for. You can find further references and an account of what is what in Martin Hyland's Towards a Notion of Lambda Monoid.


Here is a new paper that covers a similar topic. The idea is that by doing algebra in enriched categories (2-categories are like categories enriched in categories), you can talk about more fine grained semantic structure on the algebra. (I haven't read through the whole paper myself, but I know enough to see some of the ideas behind it.) The way it relates ...


A data structure Queue is very close to the concept of a List, however a Queue is a First-In-First-Out (FIFO) data structure. The available operations to interact with the List structure then, are limited to enqueue() and dequeue() (it is not a case in fact that a queue can be implemented using a List structure). In the context of Category Theory you might ...

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