# Questions tagged [terminology]

Questions of the kind "What's the name for a X that satisfies property Y?"

763
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### Terminology: are there any names for "quotients" of cellular towers in stable categories?

A cellular tower in SH or in a "more general stable homotopy category" is a chain of morphisms $\dots X^{(n)}\stackrel{g^n}{\to} X^{(n+1)}\to \dots$ along with some more data and conditions; ...

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166 views

### What's the terminology for a sequent-like variant of category?

Define a structure made of objects $A, B, C, \dots$ and morphisms $f, g, \dots$. Each morphism has a collection of domain objects and codomain objects. For simplicity we consider the domains and ...

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594 views

### English name and references for a combinatorial puzzle from Japan [closed]

I am looking for the name and references of the following puzzle.
There are n intersecting circles in a row.
At the center of the circle and at the intersection of the two circles, fill the numbers 1, ...

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**1**answer

270 views

### What's the name of this surface: $z = \exp(xy)$ [exponentialoid?] [closed]

When studying the real value exponential, I encounter the surface $z = e^{x\cdot y}$ but I don't know if it has a name. I've created a 3D applet to explore it. When I cut it by the plane
$$
(x-x_0)\...

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74 views

### Terminology for unipotent-like representations in infinite dimensions

Let $G$ be a discrete group and let $V$ be a vector space over a field of characteristic $0$ upon which $G$ acts linearly. I'm looking for the right terminology for the following situation: for all $...

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### Alternate condition for extremality

Consider a Lagrangian $L(u,p)$ where $u\in{\mathbb R}$ and $p\in{\mathbb R}^n$. Extremals of the functional
$$F[u]:=\int_\Omega L(u,\nabla u)dx$$
obey to the Euler-Lagrange equation
$${\rm (EL)}\qquad ...

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**1**answer

437 views

### Name for a Hopf algebra whose only grouplike element is the identity?

For a $k$-Hopf algebra $H$ and element $h \in H$ is called grouplike is $\Delta(h) = h \otimes h$ and $\epsilon(h)=1_k$ ($\epsilon$ is the counit). The identity $1_H$ is clearly grouplike, but in ...

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### Who is Mrs. Gerber?

This question on a theorem in information theory called Mrs. Gerber's lemma piqued my curiosity. Who is this individual, and why the "mrs." ? A quick Google search was not informative, ...

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### Why are distributions "tempered"?

Google N-Gram shows that both "tempered distribution" and "temperate distribution" are used in English, but the first version significantly prevails, and usage of the second term ...

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87 views

### Name for a "non-injective" functor [duplicate]

Let $\mathcal{C}$ and $\mathcal{D}$ be two categories. Let $F:\mathcal{C} \to \mathcal{D}$ be a functor such that, for two non-isomorphic objects $x,y \in \mathcal{C}$ we have
$$
F(x) \simeq F(y).
$$
...

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99 views

### Word for two morphisms that are equivalent up to right-composition with isomorphism

Let $f:A\to C$, $g:B\to C$ be morphisms in some category.
I call $f,g$ "equivalent" iff there exists an isomorphism $h$ such that $f\circ h=g$ (and consequently $g\circ h^{-1}=f$).
Question:...

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77 views

### Question about terminology for a class of "self-modular" mappings between rings

(In the scenario I have in mind, rings need not be unital.)
The following notion has come up in some joint work that is being written up. Let $R$ and $S$ be rings, and let $D$ be a subring of $R$. Is ...

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**1**answer

37 views

### Name for a type of assignment task

given a bipartite graph $G(U,V,E\subseteq U\times V)$ with strictly positive edge-weights; is there an established name for the the task of calculating the lightest spanning subgraph and what is the ...

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57 views

### Maximum size of vertex set with no induced connected component on more than k vertices

An independent set of a graph is a collection of vertices such that the induced subgraph consists of disconnected vertices. The maximum possible cardinality of an independent set is then called the ...

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110 views

### Pronunciation: the Erdős–Rado partition notation

The Erdős–Rado notation $a \rightarrow (b)^c_d$ is common in partition calculus / combinatorial set theory, as well as its negation $a \not\rightarrow (b)^c_d$. In that field, is there a standard way ...

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103 views

### What is the correct name of points with this property?

Let $(X, d)$ be a metric space and $x \in X$.
Suppose for all $x_1, x_2 \in X$ the following inequality holds:
$$
d(x_1, x_2) \le \max \bigl\{ d(x, x_1), d(x, x_2) \bigr\}.
$$
For example, singleton ...

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74 views

### Classification of limit points

Let $X$ be a subset of a topolgical space with no open points. Then
$$\overline{X}=X_1\sqcup X_2\sqcup X_3\sqcup X_4\sqcup X_5$$
where $X_1$ are isolated points of $X$,
$X_2$ are interior points, $X_3=...

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478 views

### Name for a Hopf algebra admitting no non-trivial 1-dimensional comodule

A Hopf algebra is called pointed if all its simple left (or right) comodules are one-dimensional. See for example this question for a discussion.
Now every Hopf algebra $H$ admits a one-dimensional ...

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74 views

### Projective limit of copies of same group w.r.t. some fixed endomorphism

In our study of automorphism groups of transcendental field extensions, we have encountered the situation where we have a group $F$ together with an endomorphism $\alpha \colon F \to F$, resulting in ...

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**1**answer

198 views

### What do shortest-path algorithms actually calculate?

The motivation for this question is a statement about the Bellman-Ford algorithm, that doesn't agree with the definition of what a path in a graph is.
On wikipedia's description of the Bellman-Ford ...

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285 views

### Is there a name for this type of matrix?

For my thesis in neural networks, I was trying to find a way to generalize a Sobel operator. I quickly thought of this:
$$
\begin{bmatrix}
a&b&c\\
d&0&-d\\
-c&-b&-a
\end{...

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114 views

### Why the name 'regular' space?

It is well known that a regular space is a topological space $X$ with these two properties:
1)All one point sets are closed.
2)For every $x\in X$ and every closed set $B$ (such that $x\notin B$), ...

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168 views

### Finding a subclass of lattices in the literature

Assume you have an algebraic problem that outputs a list of (finite) lattices on $n$ points for a given number $n$.
Question 1: Is there a way to search the internet/literature to see what exactly ...

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38 views

### Name for point sets with trivial optimal Hamilton cycle

Question:
is there an established name for sets of $n$ points in the euclidean plane whose shortest Hamilton cycles consists of the $n$ pairs of points having the $n$ smallest distances?
Names for ...

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470 views

### Name for a set of elements that fully determine a morphism

In a concrete category (i.e., where the morphisms are functions between sets), I define a base of an object $A$ to be a set of elements $M$ of $A$ such that for any morphisms $F,G:A\to B$ that ...

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1k views

### The verbs in combinatorics: Enumerating, counting, listing and all that

Two closely related, but different tasks in combinatorics are
determining the number of elements in some set $A$, and
presenting all its elements one by one.
Question: What are some works in ...

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194 views

### What is the name of this tensor?

A matrix M is usually called a hollow matrix if all of its diagonal elements are zero:
$$ M_{pp} = 0, \quad \forall \: p.
$$
We can generalize this to an $n$-way tensor T, such that:
$$ T_{p_1 \cdots ...

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320 views

### Golden ratio as a property of conic section (is it known?)

I am looking for a proof of a discovery as follows:
Let $ABC$ be arbitrary triangle and $(\Omega)$ be an arbitrary circumconic of $ABC$ let $A'B'C'$ is its tangential triangle of $ABC$ respect to $(\...

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**1**answer

257 views

### Thirteen-point conic and four-point line, are they new?

We know that Five points determine a conic and Two Points Determine a Line. Here I found a simple construct of a conic through $7$ points (in PS I note that how the conic through thirteen points) and ...

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### Is it a new discovery on conic section?

I discovered a problem in plane geometry (there are some nice special cases) as follows:
Let $ABC$ be a triangle and $\Omega$ be arbitrary circumconic. Let two points $A_b, A_c \in BC$, $B_c, B_a \in ...

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### Another betweenness centrality measure: neighbourhood centrality

Among the many centrality measures that I have heard of, I miss the following (but maybe I'm just blind).
Consider a graph $G$ with $k$ connected components $G_i$ of size $|G_i|$. The number of node ...

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64 views

### Terminology and notation for generated subgroups

I would like to think about formation of the smallest subgroup (or monoid, or whatever) $H$ of $G$ containing two given subgroups $A$ and $B$ as an operation on subgroups, and I wonder if there is a ...

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### Confusion: Normal homomorphism vs. weak*-continuous vs $\sigma$-weakly continuous

$\newcommand\M{\mathcal M}
\newcommand\N{\mathcal N}
\newcommand\A{\mathcal A}
\newcommand\B{\mathcal B}$
In Takesaki [1], I find the following theorem:
Proposition 5.13. Let $\M_1,\M_2,\N_1,\N_2$ be ...

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### What do you call such a relation between subsets in a poset

Consider a poset $(X, \geq)$. Let's define a new relation $\succsim$ on subsets of $X$: for $A, B\subseteq X$, say $A\succsim B$ if for any $a\in A$ and any $b\in B$, we have $a\geq b$.
Does such a ...

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129 views

### value (element of an algebra), constant, variable, ground and non-ground terms, free algebras : there is a need for clarification

I have been developing an algorithm to compute the congruence defined by a finite set of "generators" and a finite set of equations (in the sense of equational theories). The algorithm ...

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**1**answer

303 views

### Why "holomorphic" vertex algebra?

I have a background quite far from vertex algebras, and it seems like a vertex algebra is holomorphic if basically there is only one irreducible module, namely itself. Why is it called holomorphic?

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283 views

### Line graphs called "graph derivatives": any intuition?

Short version: in several papers, line graphs (and closely related graphs) are called graph derivatives or derived graphs; is there any intuition for such terminologies, in connection with the ...

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**0**answers

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### Representation theory terminology question

For a paper I'm writing, I need a term for a representation-theoretic concept that I'm sure someone has thought of before, so I thought I'd ask here rather than just make something up.
Let $G$ be a ...

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**1**answer

193 views

### What is the differential operator $d+d^*$ called?

The Chern-Gauss-Bonnet theorem can be deduced from the Atiyah-Singer theorem by applying it to the differential operator $d+d^*$ mapping from sum of even powers of the exterior sheaf to the sum of odd ...

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### Funny names of mathematical objects? [closed]

What are funny names of mathematical objects?
For example Mouse (set theory)

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**1**answer

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### Is there a specific name for this optimization problem?

Let $A$ be an $n\times n$ symmetric positive definite matrix with eigenvalues and eigenvectors $\lambda_1\ge\lambda_2\ge\cdots\ge\lambda_n>0$ and $v_1,v_2,\cdots,v_n$ respectively.
We know that the ...

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38 views

### Name for a curve defined by detours

define the length of the detour of going from $A$ to $B$ via the intermediate point $C$ as $\left\|C-A\right\| + \left\|B-C\right\| -\left\|B-A\right\|$
Let now
$C=(0,0)$ be located in the origin,
$\...

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**1**answer

61 views

### "Circuit rank" but for vertices

A graph's circuit rank is the minimum number of edges that have to be removed for the graph to become a tree or forest. Is there a term that represents the minimum number of vertices that we must ...

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156 views

### Can NBG be interpreted in this system that use new notation for class-abstractions?

We introduce a new symbol $\lambda$ to denote class-abstractions, and we add the following rule:
if $\phi$ is a formula that use $``\mu"$, and in which the symbol $\sf y$ doesn't occur; then: $\lambda ...

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**1**answer

138 views

### Do grammars with these properties have a name?

I'm interested in context-free grammars on a finite set of symbols where all the production rules replace a symbol by a string of length two. There is also one constraint: in the reductive direction ...

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**1**answer

218 views

### Are knot invariants topological invariants? [closed]

I am a bit confused about terminology considering topology and knot theory.
A topological invariant is considered to be a topological property that does not change under a homeomorphism of the space.
...

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84 views

### Permutation group with a nice lattice of block systems

Let $X$ be a finite set and $G$ be a transitive subgroup of the symmetric group on $X.$ Recall that a (complete) block system for this action is a partition of $X = B_1 \cup \cdots \cup B_k$ into ...

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### Reference request: Spectrum of intersection matrices

Let $P(A)$ be the set of all non-empty proper subsets of a finite set $A$. Let $M$ be a matrix indexed by the set in $P(A)$ whose $ij$ the entry is $1$ if the associated sets are disjoint and $0$ ...

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**2**answers

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### Who started the "-oid" suffix fashion in math?

There are lots of structures which have name suffixed by "oid". Off the top of my head, matroid, greedoid, perfectoid, causaloid...
Who started this? AFAIK, "matroid", by Whitney, ...

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223 views

### Given a unitary commutative ring $R$, what are the rings $R\langle x,y\rangle/(x^2-A,y^2-B,yx-a-bx-cy-dxy)$ called

We are studying the rings
$$
R \langle x, \, y \rangle\,\big/\left(x^2-A, \, y^2-B, \, yx-a-bx-cy-dxy \right)
$$
Do you know if they have a name?