TQFT (The Topological Quantum Field Theory Song)
Lyrics:
I've got a one dimensional QFT
It's pretty straightforward topologically
In this case it's just a vector space
But if you want to talk categorically
A morphism is an oriented line
Between points with a plus or minus sign
It's equivalent to "dual pairs"
And that's a category that I won't define
I just need a functor for my quantum field theory
Will it be monoidal? You bet it better be
I'll take it symmetric, but don't give me a metric
It's only topological to me
Dimension two is a little more fun
Objects are generated by S^1
Classify the surface with Morse theory
And there you've got a bordism category
Designate a vector space
As a functor that's your fate
As a groupoid it's the equivalent of
Commutative Frobenius algebras
I just need a functor for my quantum field theory
Will it be monoidal? You bet it better be
I'll take it symmetric, but don't give me a metric
It's only topological to me
Now it's time for dimension three
Knock knock whose there higher category theory
Infinite generators just won't do
So we'll take morphisms to level two
I've read all the papers
A categoric adventure
I still don't know what it means
To be "modular tensor"
I just need a functor for my quantum field theory
Will it be monoidal? You bet it better be
I'll take it symmetric, but don't give me a metric
It's only topological to me
I just need a functor for my quantum field theory
Will it be monoidal? You bet it better be
I'll take it symmetric, but don't give me a metric
It's only topological to me