4 problems

Let $k$ be a field and let $F\in LAff_k^{\sim,ffqc}$ be a schematic homotopy type. Let $i(F)$ be its image among stacks over $Hk$, and let $LParf(i(F))$ be the associated $k$-tenso…

Let $k$ be a field and let $(X\otimes k)^{sch}\in LAff_k^{\sim,ffqc}$ be the schematic homotopy type associated with a connected finite CW complex $X$, and let $LParf(X,k)$ be its…

Let $k$ be a field and let $T$ be a $k$-Tannakian Segal category. Let $\mathcal{H}(T)$ denote a $k$-Tannakian category and let $Ind(\mathcal{H}(T))$ be its ind-category with its in…

Let $A$ be a commutative ring spectrum, let $T$ be an $A$-tensor Segal category, and let $FIB_A(T)$ be its stack of fiber functors. For an $A$-Tannakian Segal category, the source…