Flatness (mathematics)

In mathematics, the flatness (symbol: ⏥) of a surface is the degree to which it approximates a mathematical plane. The term is often generalized for higher-dimensional manifolds to describe the degree to which they approximate the Euclidean space of the same dimensionality. (See curvature.)

Flatness in homological algebra and algebraic geometry means, of an object ${\displaystyle A}$ in an abelian category, that ${\displaystyle -\otimes A}$ is an exact functor. See flat module or, for more generality, flat morphism.

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