Categorizing the Abstract

[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.