Editing Linear algebraic group (section)

===Tannakian categories===
The finite-dimensional representations of an algebraic group ''G'', together with the [[tensor product]] of representations, form a [[tannakian category]] Rep<sub>''G''</sub>. In fact, tannakian categories with a "fiber functor" over a field are equivalent to affine group schemes. (Every affine group scheme over a field ''k'' is ''pro-algebraic'' in the sense that it is an [[inverse limit]] of affine group schemes of finite type over ''k''.<ref>Deligne & Milne (1982), Corollary II.2.7.</ref>) For example, the [[Mumford–Tate group]] and the [[motivic Galois group]] are constructed using this formalism. Certain properties of a (pro-)algebraic group ''G'' can be read from its category of representations. For example, over a field of characteristic zero, Rep<sub>''G''</sub> is a [[semisimple category]] if and only if the identity component of ''G'' is pro-reductive.<ref>Deligne & Milne (1982), Remark II.2.28.</ref>