Theorems in algebraic topology | Homological algebra

Acyclic model

In algebraic topology, a discipline within mathematics, the acyclic models theorem can be used to show that two homology theories are isomorphic. The theorem was developed by topologists Samuel Eilenberg and Saunders MacLane. They discovered that, when topologists were writing proofs to establish equivalence of various homology theories, there were numerous similarities in the processes. Eilenberg and MacLane then discovered the theorem to generalize this process. It can be used to prove the Eilenberg–Zilber theorem; this leads to the idea of the model category. (Wikipedia).

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Related pages

Model category | Mapping cone (homological algebra) | Free functor | Module (mathematics) | Abelian category | Simplicial homology | Mathematics | Samuel Eilenberg | Simplicial complex | Eilenberg–Zilber theorem | Theorem | Category (mathematics) | Natural transformation | Algebraic topology