Intuition of Homology, Cohomology and Homotopy

Homology 同调 is better than Euler Characteristic to differentiate manifolds with holes (eg. Torus, Klein Bottle, …).

Cohomology: ​上同调

Homology => Free Abelian Group on Set (ie Add /Subtract structure)

Co-homology => Ring Function on Set (ie Product structure)

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