# 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 ...
1 vote
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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 ...
1 vote
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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 ...
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 ...
### $(\infty,1)$-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 ...