The Brown Representability Theorem gives conditions under which a contravariant functor from the homotopy category of pointed, connected CW complexes to the category of sets is representable, meaning it agrees with the functor of homotopy classes of maps into some fixed space, provided the given functor sends wedge sums to products and satisfies a gluing condition analogous to the Mayer-Vietoris sequence. Named for Edgar Brown, it is a foundational existence result of algebraic topology guaranteeing that many naturally arising cohomology-like theories are represented by an actual topological space, called a classifying space.
Facts
Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Brown representability theorem (Wikipedia)
IntroductionQuote, Introduction
The theorem is due to Edgar H. Brown who published it in 1962.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.