7 problems

Let $p$ be prime and let $M$ be a $C_p$-Mackey functor. A projective resolution of $M$ is eventually $4$-periodic if its differentials repeat with period $4$ from some point onward…

Coinduction preservation conjecture. Coinduction restricts to a functor

External Hoyer–Mazur conjecture. For any compatible pair of indexing categories $(\mathcal O_a,\mathcal O_m)$, there is an equivalence of categories between $\mathcal O_m$-commutat…

Norm functor conjecture. There is a norm functor

Let $\mathcal{M}=\mathcal{F}_s^{\leq n}$ be the category of finite sets and surjections of cardinality at most $n$, as in Example, and let $\mathbf{C}$ be a semiadditive presentabl…

Let $\mathcal{C}$ be a small category such that its finite coproduct completion $\operatorname{fam}\mathcal{C}$ is lextensive. Let $\operatorname{Aut}\mathcal{C}$ be the category o…

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…