Nonvanishing derived limits from $\mathrm{♣}$-type principles

Combinatorial set theory provides several tools to study derived limits of certain inverse systems of abelian groups. Most known nonvanishing results for ${\lim }^n$ with $n>1$ depend on some guessing principles of the form $\mathrm{w}\mathrm{◊}(S)$ called weak diamonds. In this paper, we explore some applications of the guessing principle $\mathrm{♣}(S)$ and its weakenings instead.