# Questions tagged [definitions]

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### What is the "weight" of an automorphic form for $\mathrm{PGL}_2$?

$\DeclareMathOperator\GL{GL}\DeclareMathOperator\PGL{PGL}$I'm trying to understand what the notion of "weight" is for automorphic forms over $\GL_2(F)$ where $F$ is some number field, in ...
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### What is the mathematician's definition of the determinant? [closed]

I am trying really hard to find a good definition of the determinant. I have looked virtually every single resource online and everybody gives a different answer: sum of cofactors or minors https://...
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### Definition of “morphism of schemes that induces a bijection between irreducible components ”

$\def\sO{\mathcal{O}}\def\sF{\mathcal{F}}$On the Stacks Project there are several instances where the seemingly undefined notion of a “morphism of schemes that induces a bijection between irreducible ...
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### Measure without measurable sets

This question is a little on the softer and speculative side, so bear with me. Usually a measurable space is $(\Omega, \Sigma)$, a set $\Omega$ and sigma algebra $\Sigma$ of subsets. A measurable ...
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### Definition of locally symmetric space of reductive groups

This might seems like a bit of philosophical question and so maybe if I keep reading a bit more, I might get my answer. But, I ask nonetheless. In my attempt to study Shimura varieties, I came across ...
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### Would it be possible to propose a satisfying categorical definition for the notion of basis?

I once came across a definition for the notion of basis that was independent of the type of the algebraic structure considered (although I cannot find where). Translated into category terminology, it ...
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### Extending the class of primitive recursive functions with higher order recursion schema

I'm trying to extend the class of primitive recursive functions by extending the recursion schema over higher types. We usually define the class of primitive recursive functions by using zero function,...
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### definition of level-preserving diffeomorphism

In Hatcher, Allen; Lochak, Pierre; Schneps, Leila, On the Teichmüller tower of mapping class groups, J. Reine Angew. Math. 521, 1-24 (2000). ZBL0953.20030) page 10 we have : Up to level-preserving ...
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### Involutory vs Involutary: Are both terms correct?

I have seen references for both terms, apparently referring to the same notion of a "self-inverse function". Do both of these terms really mean the same thing? Is one a misspelling of the ...
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### Group presentation in the category of finite group

Context: I'm trying to deal with presentations in the framework of Gonthier et al. formalization of the group theory in the proof assistant Coq. It was used to machine check the Feit-Thompson odd ...
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### Potential on a quiver

I found two definitions of potential on a quiver. Selfinjective quivers with potential and 2-representation-finite algebras, Martin Herschend and Osamu Iyama 2.1 Quivers with potential. Let $Q$ be a ...
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### Analytic/synthetic distinction in mathematics besides geometry?

In a recent answer to an old MO question, I made a distinction between a "definition" of a mathematical object in the sense of axioms that characterize it, and a "definition" that ...
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### Precise definition of locally closed complex curve

In Stein Manifold and Holomorphic Mappings, by Forstnerič, I refer to Definition 8.9.9: An exposed point is a point belonging to a certain subset $\Sigma$ of $\Bbb C^2$, enjoying certain properties. ...
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### Conditions such that split coequalizers are a symmetric notion

Consider the notion of a split coequalizer (see the nLab for the definition). Note that the definition seems to be non-symmetric. Are there any conditions on the ambient category such that it becomes ...
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### Definition of a unit ball in an Euclidean subspace? [closed]

Suppose $\Lambda$ is a $3$ dimensional lattice inside $\mathbb{R}^4$ and let $E$ be the subspace $\mathbb{R}$-spanned by $\Lambda$. What exactly is meant by the unit ball in $E$? This is something ...
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I very important example of topological field theories are "BF-theories", which are usually defined as follows: Let $G$ be a Lie group with Lie algebra $\mathfrak{g}$ and let $\pi:P\to\... • 1,147 1 vote 2 answers 244 views ### Should mixed strategies in normal form games be interpreted as measurable functions or probability vectors? I have recently been stuck trying to understand how game theorists extend a normal form game (matrix game) into a game with mixed strategies (so called mixed extension). I feel like I am missing ... • 125 33 votes 5 answers 3k views ### Shapes for category theory Most texts on category theory define a (small) diagram in a category$\mathcal{A}$as a functor$D : \mathcal{I} \to \mathcal{A}$on a (small) category$\mathcal{I}$, called the shape of the diagram. ... 3 votes 1 answer 231 views ### Temporal generalization of graphs: density vs$n$and$m$? In short: we generalize graphs to the temporal case, but fail to fully preserve the usual relation between density, number of vertices, and number of edges; how to make better? Context. We propose a ... • 1,424 0 votes 1 answer 101 views ### (Seeking Definition) What Does it Mean for a Space to have Rim-Type$\alpha\$? Or the 'derivative' of a Countable Set?

I've encountered a definition in several papers, but literally none of them define the term. They all instead reference a book by Menger that has never been printed in English. The term is "rim-...
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