##  [Nearby Cycles Functor](/nearby-cycles-functor) 

  ##  [Nearby Cycles Functor](https://algebra.quantumdictionary.io/nearby-cycles-functor-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A derived functor Rψ (nearby cycles) associating to a sheaf on the total space of a family the limit of its cohomology on nearby fibers as one approaches a special or singular fiber; it records how cohomological invariants specialize and carries an action of local monodromy.