[Verse 1]
Between two worlds of mathematics
There's a bridge that carries meaning
Functors map from category C
To destination D with feeling
They take each object, transform it clean
From algebra to geometric scene
[Chorus]
Functor, functor, systematic translation
Objects flow and morphisms too
Preserve composition, keep relation
F of g compose f equals F-g then F-f it's true
Covariant keeps the arrow's direction
Contravariant flips for reflection
[Verse 2]
When arrows point from A to B
F takes f and makes it sing
F-A maps to F-B clearly
F-f connects them with a string
Identity stays identity
That's the functor's guarantee
[Chorus]
Functor, functor, systematic translation
Objects flow and morphisms too
Preserve composition, keep relation
F of g compose f equals F-g then F-f it's true
Covariant keeps the arrow's direction
Contravariant flips for reflection
[Verse 3]
Forgetful functor strips away
Group structure leaves just sets behind
Free functor builds the other way
Sets become groups, operations assigned
Homology takes topology
Returns algebraic poetry
[Bridge]
Dual space functor turns around
Vector spaces to their stars
Contravariant, arrows flip their ground
V maps to V-star near and far
Different worlds can speak as one
When functors make the translation done
[Chorus]
Functor, functor, systematic translation
Objects flow and morphisms too
Preserve composition, keep relation
F of g compose f equals F-g then F-f it's true
Covariant keeps the arrow's direction
Contravariant flips for reflection
[Outro]
Mathematics talking cross the void
Functors carry structure pure
Category theory's bridge deployed
Making abstract connections sure