# 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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### 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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### 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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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 ...