1 (one-dimensional) topological field theory-associative algebra or vector space

Two-dimensional closed string topological field theory-commutative Frobinius algebra

Free field theory of 3 (two-dimensional) anyon-solution of Yang-Baxter equation-functor entanglement invariant.

Shape field theory of 4 * * * open-closed topology —— An infinite Calabi-Hill category.

5 closed string field theory-infinite algebra.

6 * * * Zero Genus Formal Field Theory —— VOA Operator Representation of Zero Genus Riemannian Surfaces