4 problems

Let $R$ be a graded Noetherian ring, and let $\mathcal{D}(R)$ be the relevant derived or stable category with sphere object $S$. Write $\mathcal{GH}$ for the generating hypothesis,…

Let $\mathcal{A}$ be a Grothendieck abelian category, and let $D(\mathcal{A})$ be its derived category. Let $S$ denote the sphere object, and let…

Let $\mathtt{SW}^f$ be the Spanier–Whitehead category of finite spectra. The pointed $0$-sphere is $(S^0,\star)$, where $\star$ is the basepoint, and $((S^0,\star),0)$ denotes it i…

Equivariant generating hypothesis. The restriction of $\underline{\pi}_*^G(-)$ to the subcategory of finite $G$-spectra is faithful. Equivalently, if a map $f:X\to Y$ between finit…