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I think the magic acronym is CEP. See http://en.wikipedia.org/wiki/CEP_subgroup Update I've just noticed that the question is also tagged reference-request, so here's one (Google reveals many, I'm no …

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 $p \geq q$ …

Background: Let $k$ be a field and denote by $P = k[x_1,\ldots,x_n]$ the polynomial ring in $n$ (commuting) variables over $k$. A resolution of an ideal $I \lhd P$ is an exact sequence of $P$-modules …

The following object has turned up in my research recently, and it would be surprising (to put it mildly) if no one else has seen, used or studied it before. I am hoping for a name and some references …

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. …

I'm looking for a reasonable way to coherently axiomatize both length and area in the absence of a Riemannian structure, i.e., starting only with a metric space; but it's not clear how much of this wo …

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 …

Andreas Blass has produced a simple counterexample to (A) in his answer. I suspect that if your graph is flat in the sense of Andrew Stacey's answer here, then you can in fact recover it from the pair …

At least partial answers to your first two questions can be found in the brief article called Delaunay triangulations and Voronoi diagrams for Riemannian manifolds by Leibon and Letscher available her …

Fantastic question. Since I am also curious to see how Markov originally proved his theorem, I tried searching for an English version of the article. This translation definitely exists (but fails to b …

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 …

I wanted to properly cite the following awesome quote: Every mathematician has a secret weapon. Mine is Morse theory. - Raoul Bott Now this has been attributed to Bott in precisely two places th …

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 …

Background Let $\mathcal{A} = \lbrace A_0, \ldots, A_M \rbrace$ be an arbitrary sequence of finitely generated Abelian groups. It is well-known that a finite CW complex $X_\mathcal{A}$ may be construc …

I have a functor $F:C \to D$ between poset-enriched categories, and I'd like to show that the induced map on classifying spaces is a homotopy-equivalence. To this end, I am trying to establish the pre …