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De Rham decomposition theorem states that every simply-connected Riemannian manifold $M$ that admits complementary sub-bundles $T'(M)$ and $T''(M)$ of its tangent bundle parallel with respect to the ...

Because the theory of sheaves is a functorial theory, it has been adopted in algebraic geometry (both using the functor of points approach and the locally ringed space approach) as the "main theory" ...