3 problems

Let $\Sigma$ be an alphabet with a reflexive and symmetric commutation relation $\vartheta$, and let ${\rm \bf M}(\Sigma,\vartheta)$ be the associated trace monoid. Consider the tr…

Freeness conjecture. For any trace monoid $M(E,I)$ with partial action on a set $S$, the Abelian group $H_1(K_*(S), \Delta{\,\mathbb Z})$ is free.

Global-dimension extension. This is true for all Abelian categories with coproducts.