# Questions tagged [terminology]

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

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### Name for isomorphisms canonically identifying all elements in a category

Say in a category, for any two objects $A,B$, we have an isomorphism $\iota_{AB}:A\to B$ with the property that $\iota_{BC}\circ\iota_{AB}=\iota_{AC}$ and $\iota_{AA}=\mathit{id}$.
Essentially, such a ...

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### How did the term "space" in mathematics started to be understood as a set with a structure?

In mathematical literature, the term 'space' is often used to describe a set endowed with additional structure, such as a metric space or a vector space. What is the historical evolution of the ...

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### The name for a type of map between vector spaces [migrated]

Is there a name for a map $f:V \to W$ between two $\mathbb{K}$-vector spaces that is not linear map but which still staisfies
$$
f(\lambda v) = \lambda f(v), ~~~~~ \textrm{ for all } \lambda \in \...

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### A face and all its neighbors: terminology?

Suppose $F$ is a face of a 2-complex, and $F_1,\dotsc,F_n$ are the faces that are adjacent to (i.e., share an edge with) $F$. Is there a standard term for a collection of faces of the form $\{F,F_1,\...

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### Why N-1 and N-2 rings are called like that?

In the Stacks Project, Tag 032F, we find:
Definition. Let $R$ be a domain with field of fractions $K$.
We say $R$ is N-1 if the integral closure of $R$ in $K$
is a finite $R$-module.
We say $R$ is N-...

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### Names for split Lie groups

Do any of the simply connected simple Lie groups of the split real classical Lie algebras have names other than “the universal cover of _”?

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### Does there exist an established name for the exponential of surprisal (e.g. the reciprocal of probability?)

There are several different names that I know of for the exponential of the entropy of which "diversity" and "perplexity" are fairly well-established. Tom Leinster has a very ...

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### Is there a name for this family of matrices?

Let $0<a_1<a_2<\cdots<a_n$ and let $A$ be the symmetric $n\times n$ matrix with
${ij}^\text{th}$ entry $A_{ij}=\min\{a_i,a_j\}$.
For example, if $a_i=i$ for each $i\le n=5$ then
$$A=\begin{...

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### A higher-dimensional "line of curvature"?

Let $M$ be a submanifold of a Riemannian manifold $Q$, and let $\Gamma$ be a $d$-dimensional submanifold of $M$, i.e., $\Gamma^{d} \subset M \subset Q$.
Suppose that, for all (unit) normal vectors of $...

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### Who introduced the term hyperparameter?

I am trying to find the earliest use of the term hyperparameter. Currently, it is used in machine learning but it must have had earlier uses in statistics or optimization theory. Even the multivolume ...

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### Does this monoid have a name?

Fix a positive integer $n \geq 1$. Let $M$ be the monoid with generators $S=\{x_0,x_1,\ldots,x_n\}$ and relations $R = \{ \alpha x_0 = \beta x_0\colon \alpha,\beta \in S^*, |\alpha|=|\beta|\}$, where $...

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### Topological property of convergent sequences being eventually constant

Is there a name in the literature for the topological property that all convergent sequences are eventually constant?
This property seems to occur with some frequency and it would be nice to have a ...

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### Edge contractions of a graph but only along maximum cliques

Consider the following operation to an undirected graph: one is allowed to take any maximum clique and replace the clique with a single vertex which is attached to every single vertex which has an ...

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### Name for a sum of dyadic vector products

Question:
is there a name for the following operation
$$\sum_{i=1}^n\sum_{j=1}^mx_iy_j^T,\ x_i,y_j\in \mathbb{R}^k$$ i.e. for generating a square matrix that is the sum of the cartesian product of a ...

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### Referring to the countability of $\Bbb Q$ as "Cantor's first diagonal argument"

I had a discussion with one of my students, who was convinced that they could prove something was countable using Cantor's diagonal argument. They were referring to (what I know as) Cantor's pairing ...

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### What does it mean "parallel"?

I am thinking on a strict definition of the notion of parallel affine sets in a linear space and came to the following
Definition 1: An affine set $A$ is parallel to an affine set $B$ in a linear ...

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### What is the history of the term "faithful functor"?

Is it known who coined this term and what he meant? By comparison, the association between "full" and "surjective on $\mathrm{Hom}$" doesn't sound so cryptic. (I understand, of ...

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### Functors, forming pairs "coretraction–retraction", what are they called?

I asked this two months ago at MathStackExchange, but without success, so I hope that somebody at MO could help.
Let $I$ and $K$ be two categories. Let us consider two functors from $I$ to $K$:
a ...

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### Group homomorphism from $\mathrm{GL}_p$ to $\mathrm{SL}_p$ in characteristic $p$

If $k$ is a commutative field of characteristic $p>0$, then the map
$$ \theta \colon \mathrm{GL}_p(k) \to \mathrm{SL}_p(k) \colon A = (a_{ij}) \mapsto (\det A)^{-1} (a_{ij}^p) $$
is a group ...

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### What is the name of a 8-regular graph on $\mathbb Z^2$?

There are many (planar) lattices: standard square grid lattice, hexagonal lattice, triangular lattice, Lieb lattice, Kagome lattice, dice lattice...
Consider the standard square lattice on $\mathbb Z^...

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### Name of this geometric point? [closed]

Draw a triangle. At one of the vertices, draw a line through it that bisects the angle. At each of the other two vertices, draw a line through it which is perpendicular to the line that bisects its ...

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### Reflective functors?

Let $C_0\subseteq C$ and $D_0\subseteq D$ be reflective subcategories with reflection functors $r_A$ and $r_B$. For any functor $F:C\to D$, we may consider the natural transformation $r_BF\eta_A:r_BF\...

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### The canonical automorphism of the symmetric group

Let $S_n$ be the symmetric group of order $n$. Denoting simple transpositions by $\sigma_i$ the collection $\sigma_1, \dots, \sigma_{n-1}$ generates $S_n$ subject to the following relations:
$$
\sigma ...

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### A one-sided/monotone version of min/max-stable distributions -- does this have a name?

In a couple of papers I am working on (in random graph theory) I have encountered the following property of certain probability distributions, which I will describe shortly, and I am wondering if this ...

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### Is there a name for this condition on a monoid?

Suppose we have a commutative monoid ${\mathcal M}=\langle M,\otimes\rangle$ such that the usual divisibility relation $\leq_\otimes$ given by $a\leq_\otimes b\Leftrightarrow \exists c(a\otimes c=b)$ ...

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### does this relation associated with a poset have a name?

Given a partial order $P$ on a set $S$ does the set of ordered pairs $(x,y)$ in $S\times S\setminus P$ such that $P\cup\{(x,y)\}$ is a partial order have a name? (If so then it would apply to all ...

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### Name for a specific kind of regular hyper graphs

Question:
is there already an established name for the following kind of hypergaphs:
given a set $\mathfrak{V}$ with $n\lt\infty$ elements
the hyper vertices $\mathfrak{v}\subseteq \mathfrak{V}$ are ...

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### Terminology for a subtree of a rooted tree with a path boundedness property

I'm not a graph theorist, so I apologize if some of the following terminology isn't quite correct.
Let $(T,f,v_0)$ be a complete degree $d$ rooted tree (definition at the end).
Definition. Let $m\ge0$....

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### A name for "anti-symmetric" Frobenius algebras?

Let $V$ be an $N$-dim vector space and denote its exterior algebra by $\Lambda^{\ast}(V)$. The algebra $\Lambda$ has an obvious Frobenius algebra structure $B(-,-)$ given by wedgeing and then ...

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### Terminology for ordinals whose constructible level is the least one satisfying some formula

An ordinal $\alpha$ is "meta-definable" by some formula $\varphi$ without free variables if:
$$
\begin{cases}
L_\alpha \models\varphi \\
\forall\beta < \alpha \, L_\beta \not\models \...

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### Merging two composable walks in a graph

Let $G$ be a graph (i.e., an undirected graph in which we allow for loops and parallel edges). Denote by $V$ the vertex set, by $E$ the edge set, and by $\psi$ the incidence function of $G$, and let $\...

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### name for products of the form $\prod_i (1 + a_i t^i)$

In the context of generating functions, is there an established name for (infinite) products of the form $\prod_i (1+a_it^i)$, or perhaps more generally $\prod_i (1+f_i(t))$, assuming that the ...

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### Is there a name for this "generalized idempotence"?

Let $F$ and $G$ be a set (or class?) of functions, where each $f \in F$ and $g \in G$ is a function from $S$ to $S$.
Is there a name of $F$ (w.r.t. $G$) if it satisfies:
$$f_a \circ g_{i_1} \circ \...

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### Quantum exterior algebra

In Generalisation of the quantum exterior algebra the quantum exterior algebra is discussed:
$$
K\langle x_1,\dotsc x_n\rangle/(x_i^2,x_i x_j + q_{i,j}x_j x_i),
$$
with nonzero field elements $q_{i,j}...

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### Is there a literature name for this concept of a "graded metric"?

Given a space $X$, I have been thinking about a function $d\colon X \times X \times \mathbb{N} \to \mathbb{R}_{\geq 0}$ (i.e. with values that are nonnegative reals) with the properties below. One may ...

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### Name for a regularity property of $\sigma$-ideals

Let $X$ be a topological space and let $\mathcal{B}$ be its Borel $\sigma$-algebra. Suppose $\mathcal{N} \subset \mathcal{P}(X)$ is a $\sigma$-ideal, i.e. $\emptyset \in \mathcal{N}$ and it is closed ...

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### Are there any other examples where "weak" and "strong" are confused in mathematics?

What are some examples of logically weak (when there are more objects satisfying) but being called 'strong' or logically strong (when there are fewer objects satisfying) being called 'weak'?

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### Terminology for equivariant homology

The usual $G$-equivariant homology and cohomology groups of a space $X$ with $G$-action are given by the Borel construction:
$$H_\ast^G(X)=H_\ast((X\times EG)/G),$$
$$H^\ast_G(X)=H^\ast((X\times EG)/G)...

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### Is there a name for this variant of the category of elements of a profunctor?

Let $\mathsf{C}$ be a category and let $P : \mathsf{C}^{\text{op}} \times \mathsf{C} \to \mathsf{Set}$ be a functor.
Let $\mathsf{E}$ be the category whose:
objects are pairs $(X,x)$, where $X$ is an ...

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### Standard terminology for node in tree with multiple children

Is there a standard terminology for a node in a tree that has multiple children?
For instance, in describing in perfect tree in $\omega^{< \omega}$ how would you describe the nodes that are ...

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### What does it mean to have a number of size $B$?

I have a really stupid question that I don't seem to know the answer to and have been too embarassed to ask. In some number theory papers, I encounter sums of the form $$\sum_{\substack{{x \asymp B}\\...

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### Decomposing a set of integers as a union of well-separated (discrete) intervals

Let a discrete interval be a set of the form $\{x \in \mathbb Z \colon a \le x \le b\}$ with $a, b \in \mathbb Z \cup \{\pm \infty\}$. Then define the boxing dimension $\text{bim}(S)$ of a set $S \...

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### Name of a Frobenius-like method for ODEs

Mike McNulty, who is a postdoc working with me, showed me the following trick for looking at asymptotic behavior of ODEs near singular points that he found; my question: does it have a well-known name ...

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### Terminology for discrete subgroups of PSL(2,k), where k is a non-archimedean local field

$\DeclareMathOperator\PSL{PSL}$I'm asking about terminology for discrete subgroups of $\PSL(2,k)$, where $k$ is a non-archimedean local field.
As it is rather clumsy to have to use such expressions ...

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### Presentationally finite group "extensions"

Fix a group $G$ and fix a presentation of $G$ as $\langle X\mid R\rangle$. A presentationally finite extension of $G$ is any group that can be presented as $H=\langle X\cup X'\mid R\cup R'\rangle$, ...

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### Does anybody know this paperfolding curve?

In experiments with paperfolding curves, I've constructed an interesting example I cannot find anywhere else.
It is constructed like the “terdragon", where every time the strip is folded to the ...

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### Terminology associated with mathematical induction

In "Number: The Language of Science" (1930), Tobias Dantzig refers to what we call the base case of mathematical induction as "the induction step" (and refers to what we call the ...

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### Overloading of the word "local" in category theory

The word "local" in category theory does not seem to have a precise definition in itself but it often appears as part of other terminology. To my understanding, it is then used in the ...

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### In knot theory, what is this link property and how to detect it: "linkings between components separate nicely"

The following could be made more general (see below), but let's focus on a link $L$ that consists of three components (closed curves) $\gamma_1,\gamma_2,\gamma_3\subset\Bbb R^3$.
Call $L$ a necklace ...

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### $(\infty,1)$-topoi generated by $(n,1)$-categories

A (1,1)-topos (i.e. an ordinary Grothendieck topos) is called localic if the following two equivalent conditions hold:
It is the category of sheaves on a (0,1)-site with finite limits$^*$ (i.e. a ...