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Q&A for professional mathematicians
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I hope everyone is doing well. Let $K \subset \mathbb{R}^n$ be a centrally symmetric convex body $(K = -K)$. Denote by $K \mid H$ the orthogonal projection of $K$ onto $H$, where $H$ is an $n - 1$
Mathoverflow.net news digest
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3 months
Placing $n \cdot m$ coins on an $n \times n$ board generalizing the $n$-queens p...
It is a well known fact that, with the exception of $n = 2$ and $n = 3$, it is possible to place $n$ queens on an $n \times n$ chessboard that cannot attack each other.
The fact that the queens cannot attack each other boils down to the fact that there are no more than $1$ queens on any $0^{\circ}$ horizontal line, no more than $1$ queens on any $90^{\circ}$ vertical line, no more than $1$ queens on any $45^{\circ}... -
15 years
How different category theories relate
Continuing about this my question.
Mac Lane "Categories for the Working Mathematician" and "Abstract and Concrete Categories. The Joy of Cats" use different set theory foundations.
How one to transfer theorems between these two different systems? That is if a theorem is proved in one of these two systems what can be inferred in the other?... -
4 years
Gershgorin's 2nd theorem (disjoint circles): elementary proof?
Let $A \in \mathbb{C}^{n\times n}$ be a complex matrix. We let $a_{i,j}$ be the $\left(i,j\right)$-th entry of $A$ for all $i, j \in \left[n\right]$ (where $\left[n\right]$ denotes $\left\{1,2,\ldots,n\right\}$). For each $i \in \left[n\right]$, we define...
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0 days
Hypersheaves vs $\infty$-topos
I'm trying to understand the following two 'homotopy coherent' versions of sheaves.
$\infty$-topoi: In my understanding, this is supposed to capture $\infty$-sheaves on an $(\infty, 1)$ site. $\infty$-sheaves are a subcategory of the $\infty$-category of (sSet-valued) presheaves on a quasicategory, $\mathrm{Psh}(\mathcal{C}^{op}, sSet...
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