##  [Synthetic Differential Geometry](/index.php/synthetic-differential-geometry) 

  ##  [Synthetic Differential Geometry](https://puremath.quantumdictionary.io/synthetic-differential-geometry-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A categorical, axiomatic reformulation of differential geometry in which infinitesimals are represented by nilpotent elements inside a suitable topos or algebraic setting; derivatives and tangent vectors are treated algebraically via axioms (e.g., Kock–Lawvere) rather than as limits, enabling coordinate-free, algebraic manipulation of smooth structures.