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 ...
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 ...
So one way to categorify the natural numbers is to replace them with vector spaces. Then the dimension of the vector space reproduces the natural number. More generally you can categorify integers to ...