137 \begin{abstract} -- enter abstract text here -- \end{abstract}

   137 \begin{abstract}

   138 We explain the need for new axioms for topological quantum field theories that include ideas from derived categories and homotopy theory. We summarize our axioms for higher categories, and describe the `blob complex'. Fixing an $n$-category $\cC$, the blob complex associates a chain complex $\bc_*(W;\cC)$ to any $n$-manifold $W$. The $0$-th homology of this chain complex recovers the usual TQFT invariants of $W$. The higher homology groups should be viewed as generalizations of Hochschild homology. The blob complex has a very natural definition in terms of homotopy colimits along decompositions of the manifold $W$. We outline the important properties of the blob complex, and sketch the proof of a generalization of Deligne's conjecture on Hochschild cohomology and the little discs operad to higher dimensions.

   139 \end{abstract}