MathOverflow

I warn that this is potentially a dumb question because I am going to asking for motivation for this definition after stripping away the original motivation.
Regardless, tLet $\mathscr C$ be a category, and suppose we take a pre-stack $\mathscr F$ to be a contravariant pseudo-functor from $\mathscr C$ to the $2$ (by which I mean $(2,1)$ category) category of groupoids $\operatorname{Grpd}$. My question is...

We use $\mathbb{G}(l,k+l)$ to denote the Grassmannian consisting of all $l$-vector in $\mathbb{C}^{k+l}$. Given a $k$-vector $v$ in $\mathbb{C}^{k+l}$, let $H_{v}$ be the set of all $l$-vector in $\mathbb{C}^{k+l}$ that is not transverse to $v$. It is...

I want to show the following asymtotic estimate in Hardy space over $\mathbb{R}^n$: Let $a\in \mathbb{R}^n$. I want to show the function$$f(x)=\mathbb{1}_{B(0,1)}-\mathbb{1}_{B(a,1)}$$is asymtotic to $\ln|a|$; that is,$$||f||_{\mathcal{H}^1}\sim \ln...

Let AC denote the Axiom of Choice. Let PP denote the so-called "Partition Principle" which states that "If S is a non-empty set and T is a non-empty set of pairwise disjoint subsetsof S, then S can be mapped onto T". It is well known that "AC implies...