The functor $\mathsf{Sym}_A$ is left adjoint to the forgetful one $A\text-\mathsf{cdga}_{\leq0}\to A\text-\mathsf{dg\text-mod}_{\leq0}$, where $A\in k\text-\mathsf{cdga}_{\leq0}$. I have troubles computing $\mathsf{Hom}_{k\text-\mathsf{cdga}_{\leq0}}(\mathsf{Sym}_A(X),B)$. Intuitively, it seems ...

Problem. Let $G$ be a graph with a $K_5$ minor. Prove that $G$ contains either a $K_5$ or a $K_{3,3}$ topological minor. I'm having a hard time believing this result. Consider the graph $G$ obtained from $K_5$ by replacing one of its vertices with a cycle of length 4: Where is the $K_5$ or $K...

I'm having some confusion with proposition $1.72$ of the Diestal book on Graph Theory which states that (ii) If $\Delta(X) \leq 3$, then every $MX$ contains $TX$ thus every minor with maximum degree $3$ is also it's topological minor. I feel as if i've found a counter-example which of course ...

If $H$ has maximum vertex degree at most $3$ (so $\Delta(H)\leq 3$) and $H$ is a minor of $G$, then $H$ is a topological minor of $G$. The converse follows by definition. However, most sources state this proposition without a proof. Any help is greatly appreciated.

A topological minor of $\Gamma$ is a graph, obtained form a subgraph of $\Gamma$ by collapsing paths of degree-two vertices to single edges A minor of $\Gamma$ is a graph, obtained form a subgraph of $\Gamma$ by arbitrary edge contractions. It is not hard to see, that any topological minor is ...