11 problems

Conjugacy conjecture. There exists an invertible element $x\in R$ such that

Let $\mathcal{E}$ be an exact category, and suppose that there exists an integer $n\geq 0$ for which $\mathcal{E}$ has at least one $n$-tilting subcategory. Let…

Let $\mathpzc{E}$ be a monoidal AdMon-elementary exact category. Let $\mathfrak{P}$ be an operad and $\mathfrak{C}$ a cooperad, and let $\alpha:\mathfrak{C}\rightarrow\mathfrak{P}$…

Let $\mathcal{E}$ be an exact category, and let $\operatorname{\mathsf{AR}}(\mathcal{E})$ denote the subgroup generated by its Auslander–Reiten conflations inside the subgroup…

Product conjecture for Grothendieck–Witt spectra. There is a canonical equivalence of spectra

Let $k$ be a complete discrete valuation ring with uniformizing element $l\in k$. For objects $X,Y\in\mathcal E_{k,0}^{G/H}$, suppose that the natural maps … are surjective for all…

Let $k$ be a complete discrete valuation ring with uniformizing element $l\in k$. Let $c\colon G\longrightarrow k^*$ be a continuous multiplicative character of a profinite group…

Let $\mathscr A$ be a profinitary exact category, and let $\Gamma_{\mathscr A}$ be its Grothendieck monoid. A monoid is locally finite if, for every $\gamma\in\Gamma_{\mathscr A}$,…

Let $\mathcal{A}$ be an exact category. Write $S(\mathcal{A})$ for the geometric realization of the simplicial category $iS_{\bullet}(\mathcal{A})$ given by Waldhausen's…

Adámek–Lawvere–Rosický conjecture. A complete and sifted-cocomplete category should be algebraically exact if and only if it is Barr-exact, finite limits commute with filtered coli…

Let $\mathcal C$ be a skeletally small abelian category, and let … be the category of exact functors $\mathcal C^{\mathrm{op}}\to\operatorname{Ab}$. Equip $\mathcal A$ with its can…