##  [Tannaka Duality](/tannaka-duality) 

  ##  [Tannaka Duality](https://mathlogic.quantumdictionary.io/tannaka-duality-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A reconstruction correspondence that recovers a (pro-)algebraic group (or group scheme) from the tensor category of its finite-dimensional linear representations together with a choice of fibre functor to vector spaces; conversely, the category of representations is the primary invariant of the group.

 

 

 

 

 





 

 



 ##  [Tannaka Duality](https://algebra.quantumdictionary.io/tannaka-duality-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A duality principle and reconstruction theorem that recovers an algebraic object (such as a proalgebraic group, group scheme, or Hopf algebra) from a suitably rigid tensor category of its linear representations together with a fiber functor to vector spaces.