Cocharacter lattice of an algebraic torus
= Cocharacter lattice of an algebraic torus
{title2=$N$}
The cocharacter lattice $N=\operatorname{Hom}(\mathbb G_m,T)$ is dual to the <character lattice of an algebraic torus> under composition:
$$
\langle m,n\rangle\in\operatorname{Hom}(\mathbb G_m,\mathbb G_m)\cong\mathbb Z.
$$