  We give a universal construction of a derived affine group scheme and its
representation category from a symmetric monoidal infinity-category, which we
shall call the tannnakization of a symmetric monoidal infinity-category. This
can be viewed as infinity-categorical generalization of the work of
Joyal-Street and Nori. We then apply it to the stable infinity-category of
mixed motives equipped with the realization functor of a mixed Weil cohomology
and obtain a derived motivic Galois group whose representation category has a
universality, and which represents the automorphism group of the realization
functor. Also, we present basic properties of derived affine group schemes in
Appendix.
