[Verse 1]
In the world of mathematics, there's a pattern we can see
Objects and their arrows form a grand geometry
Sets with functions, groups with maps that keep their structure true
Categories show us how these universes grew
[Chorus]
Objects, morphisms, composition law
Identity for each, that's what we saw
Associative rules and identity holds
Category theory, the story unfolds
Maps between maps, structure preserved
Mathematics studying itself observed
[Verse 2]
Take your sets and functions, that's where we begin
Groups with homomorphisms, let the patterns spin
Rings and topological spaces, vectors in a field
Every universe of structure has the same revealed
[Chorus]
Objects, morphisms, composition law
Identity for each, that's what we saw
Associative rules and identity holds
Category theory, the story unfolds
Maps between maps, structure preserved
Mathematics studying itself observed
[Bridge]
From A to B, from B to C
Composition flows so naturally
Every object has its own identity
The laws of categories set mathematics free
[Verse 3]
Modules over rings, continuous maps in space
Linear transformations, each finds its rightful place
The pattern stays the same though objects change their face
Category theory shows the universal grace
[Chorus]
Objects, morphisms, composition law
Identity for each, that's what we saw
Associative rules and identity holds
Category theory, the story unfolds
Maps between maps, structure preserved
Mathematics studying itself observed
[Outro]
Categories connect what seemed apart
Mathematics has a beating heart
Structure flows through every part
This is where the patterns start