### Our Raison D’être

#### Posted by David Corfield

Marni Sheppeard reports from the AustMS2006 conference, which, as anyone who knows about Australian mathematics might expect, is holding a category theory session. Dominic Verity is giving one of the talks, in which he considers the *raison d’être* for higher category theory, and so by extension that of the Café. Of course, we also come here for the coffee.

## Re: Our Raison D’être

Dominic Verity wrote:

What would you all understand under “non-abelian”?

Am I mislead if I feel that if “non-abelian” cohomology is the raison d’être of anything, then of higher

groupoidtheory (only)?I have never seen a general definition: “non-abelian cohomology is…”, but all the examples I know are of the form:

By removing the requirement that $C$ be a 1- and $T$ be an $n$-groupoid (in some weak sense), we can get something even more general, which I wouldn’t in general compare to “abelian” anymore.

Also, is the idea really that the concept $[C,T]_\sim$ is the raison d’être of category theory? Or is my concept of non-abelian cohomology above too narrow-minded?