[Verse 1]
In category land where functors roam
There's a bridge between each distant home
F takes objects left to right
While G brings them back to sight
When hom sets match in perfect dance
That's adjunction's sweet romance
[Chorus]
F left G right, adjoints in flight
Hom D of F A B equals Hom C A G of B
Yoneda whispers secrets true
Nat transforms reveal what functors do
Left kills limits, right saves all
Category theory standing tall
[Verse 2]
Representable speaks in hom-set tongue
From C-op to Set the song is sung
Hom of dash A tells the tale
Where contravariance will never fail
Each object gets its signature voice
In the functor's faithful choice
[Chorus]
F left G right, adjoints in flight
Hom D of F A B equals Hom C A G of B
Yoneda whispers secrets true
Nat transforms reveal what functors do
Left kills limits, right saves all
Category theory standing tall
[Bridge]
Yoneda embedding fully faithful and true
Y maps C into presheaf view
Natural transformations from hom to F
Give you F of A, no more no less
The lemma shows what's hiding there
In functor's categorical lair
[Verse 3]
Left adjoints crush the colimits down
Right adjoints make limits stick around
Preservation flows through morphism streams
While exactness fulfills our wildest dreams
Cocontinuous on the left side
Continuous where right adjoints hide
[Chorus]
F left G right, adjoints in flight
Hom D of F A B equals Hom C A G of B
Yoneda whispers secrets true
Nat transforms reveal what functors do
Left kills limits, right saves all
Category theory standing tall
[Outro]
From hom-sets to embeddings deep
These seven laws are ours to keep
Adjunction, Yoneda's mighty call
Seven equations rule them all