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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}...

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?...

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...

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...