가사
[Verse 1]
Sets, rings, topological spaces,
In a single framework, they find their places,
Outside the reign of set theory, an alternative,
Category theory emerges, definitively creative and innovative.
[Verse 2]
Morphisms, as links, in diagrams depicted,
Mono, Epi, Iso, Bi, Endomorphisms,
As well as retractions and sections,
Are connected by arrows depicting morphism directions.
[Chorus]
A class, object, and binary operation,
Oh, category theory, what a revelation,
A language to unify all of math's creation,
Oh, in the realm of abstraction, you're our foundation.
[Verse 3]
Universal properties, they guide the way,
In categories, where concepts sway,
From products to coproducts, they display,
Invariance in a categorical ballet.
[Verse 4]
Adjunctions and monads, they hold the key,
To understanding structures, both wide and free,
Monad laws ensure harmony's decree,
In category theory's vast, unfettered sea.
[Chorus]
A class, object, and binary operation,
Oh, category theory, what a revelation,
A language to unify all of math's creation,
Oh, in the realm of abstraction, you're our foundation.
[Chorus]
A class, object, and binary operation,
Oh, category theory, what a revelation,
A language to unify all of math's creation,
Oh, in the realm of abstraction, you're our foundation.
[Verse 5]
Topos theory, a realm profound,
Where logic and sets are deeply bound,
Sheafification, topos logic's strong,
Connecting concepts, where they belong.
[Verse 6]
Homotopy theory, where paths connect,
Using categories, new ideas reflect,
Homology and cohomology, in prospect,
In a categorical symphony, where concepts intersect.
[Chorus]
A class, object, and binary operation,
Oh, category theory, what a revelation,
A language to unify all of math's creation,
Oh, in the realm of abstraction, you're our foundation.
[Outro]
Category theory, a tapestry of structure,
Unraveling relations with each functor,
From the foundations to the stars above,
In mathematics, you're truly in love.
[Chorus]
A class, object, and binary operation,
Oh, category theory, what a revelation,
A language to unify all of math's creation,
Oh, in the realm of abstraction, you're our foundation.
[Chorus]
A class, object, and binary operation,
Oh, category theory, what a revelation,
A language to unify all of math's creation,
Oh, in the realm of abstraction, you're our foundation.
[Outro]
Category theory, a tapestry of structure,
Unraveling relations with each functor,
From the foundations to the stars above,
In mathematics, you're truly in love.
[Outro]
Category theory, a tapestry of structure,
Unraveling relations with each functor,
From the foundations to the stars above,
In mathematics, you're truly in love.
