9 problems

Let $\mathbf{bO}$ denote the global space that is the direct limit of the global classifying spaces $\mathbf B O(n)$, and regard $\mathbf{bO}$ also as an orbispace through the func…

Let $G$ be a finite group. Write $\mathbf B G\in\mathrm{OrbSpc}$ for its classifying orbispace and $\mathbf B G\in\mathrm{GloSpc}$ for the corresponding global classifying space. C…

Let $\mathrm{OrbSpc}$ be the category of orbispaces, let $\overline{\mathrm{OrbSpc}}$ be its enlargement obtained by gluing cells under arbitrary maps, and let $\mathrm{GloSpc}$ be…

Global-space full-faithfulness conjecture. For $X\in\mathrm{OrbSpc}^f$ and $F\in\mathrm{GloSpc}$, the set $\operatorname{Hom}(X,F)$ coincides with the morphisms from the image of…

Let $R(*)$ be the terminal object of $\mathrm{RepOrbSpc}$, and let $\mathrm{Rep}\{\mathbf B G\}$ be the full subcategory spanned by the classifying orbispaces of finite groups. Poi…

Let $R(*)$ be the terminal object of $\mathrm{RepOrbSpc}$, and let $\mathrm{RepOrbSpc}_{R(*)/}$ denote the under-category of $R(*)$. Pointed-orbispace under-category conjecture. Th…

Let $X$ be a metrizable locally tame topological orbifold, meaning a topological orbifold satisfying the local tameness condition used in the paper. Finite orbispace realization co…

Let $R:\mathrm{OrbSpc}\to\mathrm{RepOrbSpc}$ be the right adjoint to the forgetful functor $\mathrm{RepOrbSpc}\to\mathrm{OrbSpc}$, and let $R(*)$ denote its value on the point. A r…

A compact orbispace is a compact topological stack which admits a cover by open substacks of the form $Y/\Gamma$, where $\Gamma$ is a finite group acting continuously on a topologi…