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In this article, the generalized gravity theory with the curvature, torsionand nonmetricy was studied. For the FRW spacetime case, in particular, theLagrangian, Hamilatonian and gravitational equations are obtained. Theparticular case $F(R,T)=\alpha R+\beta T+\mu Q+\nu{\cal T}$ is investigated indetail. In quantum case, the corresponding Wheeler-DeWitt equation is obtained.Finally, some gravity theories with the curvature, torsion and nonmetricity arepresented.

Generalized gravity theory with curvature, torsion and nonmetricity