# Questions tagged [categorification]

The tag has no usage guidance.

56 questions
Filter by
Sorted by
Tagged with
310 views

### What are meromorphic line bundles?

Initially I wanted to call this question "Categorification of meromorphic functions?" but discovered so many questions about categorification that I became scared and decided to replace it ...
107 views

### An alternative (?) approach to differential ringoids

Recall that a derivation on a ring $R$ is a function $\partial:R\to R$ satisfying the Leibniz rule $$\partial(ab)=\partial(a)b+a\partial(b),$$ and a differential ring is just a ring equipped with a ...
1 vote
112 views

106 views

239 views

### Reference Request: The Categorification of $\mathbb{Z}$ as cochain complexes of vector spaces

Just as the fact that a categorification of $\mathbb{N}$ is the category of finite dimensional vector spaces, a categorification of $\mathbb{Z}$ (in my mind) is the category of bounded cochain ...
1k views

5k views

### Examples of categorification

What is your favorite example of categorification?
747 views

### Are homological knot invariants of finite type?

It is well known that, after a change of variables, the quantum knot invariants (Jones, HOMFLY, Kauffman, etc.) can be written as power series whose coefficients are finite type (i.e., Vassiliev) ...
397 views

### Categorifying the group representations

I've heard about this construction on the lecture about higher representation theory: Given a Lie algebra $g$, one constructs $\mathcal A$, a category whose $K_0$ is the universal enveloping ...
12k views

### What precisely Is "Categorification"?

(And what's it good for.) Related MO questions (with some very nice answers): examples-of-categorification; can-we-categorify-the-equation $(1-t)(1+t+t^2+\dots)=1$?; categorification-request.
2k views

### What structure on a monoidal category would make its 2-category of module categories monoidal and braided?

So, many of us know the answer to "what kind of structure on an algebra would make its category of representations braided monoidal": your algebra should be a quasi-triangular Hopf algebra (maybe if ...
668 views

### What's the right object to categorify a braided tensor category?

The yoga of categorification has gained a lot of popularity in recent years, and some techniques for it have made a lot of progress. It's well-understood that, for example, a ring is probably ...
Some physicists have told me that if you think about an extended n-dimensional TQFT $F$, then the decategorification is given by $F'(X)=F(X\times S^1)$, which I believe they call "compactification on ...