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> What are some relations between the existence of Motivic t-structures and Motivic galois groups?
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I heard that indeed the existence of the Motivic t-structure implies the isomorphism between Ayoub's Motivic galois group and Nori's. Is this correct?



Relations between Motivic Galois groups and Motivic t-structure?
The argument sketched in Example 3.20 of [J. P. Pridham, *Tannaka duality for enhanced triangulated categories*, [arXiv:1309.0637](http://arxiv.org/abs/1309.0637)] demonstrates the comparison assuming the existence of the motivic t-structure.


On the other hand, an unconditional proof is given in [Utsav Choudhury, Martin Gallauer Alves de Souza, *An isomorphism of motivic Galois groups*,  [arXiv:1410.6104](http://arxiv.org/abs/1410.6104v2)].


