I have two graded (generally noncommutative!) algebras $A$ and $B$ given by generators and homogeneous relations. Given two graded algebra homomorphisms $f,g:A\to B$ which are given by their values on the generators. I want to be able, for every fixed $n\in\mathbb N$, to know whether the kernel of $A$ in degree $n$ is contained in the kernel of $B$ in degree $n$.