The n-Category Café

What would be nice is a page of things where we almost know how to categorify it, and why it would be cool if we did. Because nearly every mathematical structure could be categorified.

And I’ve never heard of satisfacienda (at least, not as an English word), so I’d say that “Things to be categorified” is a much better title than either of the other suggestions.

‘categorification’ (not ‘categorifaction’), so ‘categorificienda’ (not ‘categorifacienda’).

Although ‘things to be categorified’ also works.

How about “Categorigenda?” (like agenda and corrigenda … who’s to say the verb wasn’t categorigio/categorigere? (apart from being, as you say, at least as much greek as latin)

Categoriata? Categorialia? Categorientals? Precategories? Kittegories? Pussigories? Whose Ox is Catigored?

So the Yoneda embedding of a category $\mathcal{C}$ to $F(\mathcal{C}) = [\mathcal{C}^{op}, Set]$ is a 2-coalgebra for the 2-endofunctor $F$.

Like with the powerset functor there surely can’t be a terminal 2-coalgebra for $F$. What about $G(\mathcal{C}) = 1 + A \times \mathcal{C}$, where $A$ is a fixed category? I suppose the terminal 2-coalgebra would have as objects finite or infinite lists of objects of $A$ with lists of arrows of $A$ as morphisms.

Categorificanda, from the well known latin verb categorificare. ;)

It’s a Golden Oldie, but I like it —

• Categorical Imperatives