| In joint work with David Blanc and Jim Turner, the speaker has considered different ways to decompose diagram (Andre-Quillen) cohomology. The current approach involves constructing a notion of ideal for a small category, which leads to a certain topological space roughly analogous to Spec of a (commutative) ring. Over this space, diagram cohomology of restrictions yields a sheaf, which is really a general decomposition result. In addition, there is a promising ``structure sheaf" over this space, as in the construction of affine schemes, whose values consist of localizations of the category at an ideal. |
