Flatness (mathematics) | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-10-07

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Flatness_(mathematics)





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SUMMARY
=======
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 
  
    
      
        A
      
    
    {\displaystyle A}
   in an abelian category, that 
  
    
      
        −
        ⊗
        A
      
    
    {\displaystyle -\otimes A}
   is an exact functor.  See flat module or, for more generality, flat morphism.