Abstract

In the context of abelian groups, multiextensions are to multilinear maps what extensions are to homomorphisms. Multiextensions can be defined for categories and stacks, where they classify functors which are additive in each variable. Applications and motivations stem from the problem of describing various kinds of categorical rings and the cohomology theories that arise as their characteristic classes, such as those of Hochschild and Mac Lane. In this part we'll look at the various cohomology of rings, with a bit of history. Then we'll see how, in certain degrees, these are realized by categorical rings, already seen in Part I. This will pave the way to discuss multi extensions.