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Is there a name/reference for the following object? We have a vector space $V$ over some field with two associative bilinear operations $\circ,*:V \times V \to V$ which satisfy the interchange law, i. …

Let $X$ be a set and $(T,\cdot)$ an abelian group. Is there a category of $T$-dynamical systems on $X$ which yields useful information about $X$ and $T$? More precisely, is there a category whose obj …

I'm fairly confident that the following assertion is true (but I will confess that I did not verify the octahedral axiom yet): Let $T$ be a triangulated category and $C$ any category (let's say small …

Let $f,g:\mathbb{R}^m \to \mathbb{R}^n$ be two smooth functions and let $k$ be a strictly positive integer. Write $f \sim_k g$ if at each point in the domain, the determinants of all $k \times k$ mino …

Let $B \subset \mathbb{R}^n$ be a collection of $n$ (not necessarily independent) unit vectors which we will label $v_1,\ldots, v_n$ for convenience. The cone $K_B \subset \mathbb{R}^n$ associated to …

In a context slightly more general than yours, this is called the right Ore condition. If you treat your poset as a category where there is a unique morphism from $p$ to $q$ if and only if $p \geq q$ …

A recent project has forced me to consider a rather special object in a rather nasty category. Consider any category $\mathcal{C}$ which has image objects, meaning for each morphism $f: x \to y$ the …

Let $(X,\Sigma,\mu)$ be a measure space and consider a family of $\mu$-measurable functions $f_i:X \to \mathbb{R}$ for $i$ lying in some index set $I$. Define $$f(x) = \inf_{i \in I} f_i(x)$$ I think …

Since this area is developing rather quickly, there is a dearth of canonical references that would satisfy basic pedagogical requirements. If I were teaching a course on this material right now, I wou …

Fix a number $n$, and define $\gamma(n)$ to be the number of simplicial complexes on $n$ unlabeled vertices up to homotopy equivalence. It is unlikely that an explicit formula exists, but what is know …

Your question is precisely the subject of Justin Curry's recent preprint. Bottom line: if you agree to identify functions $f,g:[0,1] \to \mathbb{R}$ whenever they have the same merge-tree, then ther …

The name of that article changed (a lot, it seems): the information you seek is in the paper Doctrinal Adjunction by Kelly. It lies on page 257 of the collection Category Seminar, Number 420 of Le …

If you want the first use of the term "constructible" in this context, then your reference to Mel Hochster's work is right-on. But if you want the actual notion, then things get slightly hazy. I think …

Here is a cool new (and very readable) preprint which uses the second barycentric subdivision (as discussed in Zhen Lin, Fernando Muro and Peter May's comments) to construct a cofibrantly generated mo …

Bad News The answer to Q3 as stated is no. Let $X$ be the Michael line, and let $Y$ be the closed subset consisting of all the rationals. Then, there is no bounded linear extension $C(Y,\mathbb{R}) \t …