Construction: given a friendly group $G$ - for example an old favourite $SL_{n}$ - we can learn something of its structure by considering how it acts on a vector space, namely by considering a representation of $G$. We can take this a step further by considering the category of all (nice enough) representations of our friend $G$ and ask ourselves if this category itself displays some interesting structure. Our answer will come in the form of certain diagrammatic categories and will hopefully explain the picture to some extent.

Reconstruction: time permitting, we’ll also consider the reverse question: knowing the category of representations of a group $G$, under what circumstances does this category hold enough information to completely reconstruct the group $G$?