# Topological Quantum Field Theory

For a topological quantum field theory, $Z:Cob(n)\to Vect(\mathbb{C})$ why is it that typically $Z(\emptyset)\cong \mathbb{C}$? Is that just the definition that makes everything work?

Look at disjoint union of a manifold and an empty manifold. So you're getting $V$ and $C$ so when you combine you better get $V$ again. This is the monoidal unit requirement.