nLab Higher Algebraic Structures and Quantization

The article

• Daniel Freed, Higher Algebraic Structures and Quantization, Commun.Math.Phys. 159 (1994) 343-398 (arXiv:hep-th/9212115)

and the companion

• Daniel Freed, Quantum groups from path integrals (arXiv:q-alg/9501025)

contain an early proposal that (topological) quantum field theory should have an “extended” or “multi-tiered” formulation which involves not just vector spaces of phases/staes in codimension 1, but also (n-k)-vector spaces in codimension $k$.

This is a first indication of the structure that was later made precise by Jacob Lurie in On the Classification of Topological Field Theories by extended field theory in terms of (infinity,n)-functors on the (infinity,n)-category of cobordisms.

See at higher category theory and physics for more comments.

category: reference