The definitions tag has no wiki summary.

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### Lattices: why require bilinear form to be integral?

This is a quite localized question, but I hope it won't be closed as unfit to MO. Well, a lattice $\Lambda$ in $\mathbb{R}^n$ is a discrete subgroup generated by a basis. Such a lattice gets a ...

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**3**answers

745 views

### Transitive closure of multigraphs

The transitive closure of a directed graph, is another directed graph which encodes the reachability of nodes from other nodes. If $G$ is a graph, the edge $(v_1,v_2)$ is in it's transitive closure ...

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453 views

### Euclidean Function at 0

In a few places where I have looked the Euclidean Function of a Euclidean Domain is only being defined for non-zero elements. I am teaching an undergraduate course and I am trying to make things ...

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**18**answers

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### Can a mathematical definition be wrong?

This question originates from a bit of history. In the first paper on quantum Turing machines, the authors left a key uniformity condition out of their definition. Three mathematicians subsequently ...

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**3**answers

857 views

### Is there an intrinsic definition of fractal (i.e. not embedded in euclidean space)?

Long ago, manifolds were embedded subsets of euclidean space defined by polynomials. Later, using the gluing of open sets, people realized they could define manifolds intrinsically. And in certain ...

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**1**answer

791 views

### Is there a mathematical object called “ivy”?

As the title says, is there a mathematical object referred to as "ivy" or "ivy type" or similar?
I have a type of graph where this name fits perfectly, but I don't want it to clash with something ...

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**2**answers

279 views

### Do you know of any asymmetric, nonparametric measure of dependence?

A measure of dependence is a way to assign a number (usually normalized between 0 and 1) to a couple of random variable, such that $\delta(X,Y)=0$ if and only of $X$ and $Y$ are independent, and ...

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**1**answer

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### What is Serre's condition (S_n) for sheaves?

The Serre's condition $(S_n)$, especially $(S_2)$, has been mentioned in a few MO answers: see here and here for example. I am pretty sure I have seen it in other questions as well, but could not ...

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**4**answers

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### Definition of forgetful functor

I was wondering if it is possible to make a formal definition of what it means for a functor to be forgetful. That is, using only the terminology of categories. I have seen so many examples of ...

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**5**answers

355 views

### Strings and “co-subsequences”

Let $S$ be a string over some alphabet $\Sigma$. It is well known that a substring of $S$ is commonly defined as a sequence of contiguous elements from $S$, while a subsequence of $S$ is a sequence ...

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**2**answers

2k views

### Category Theoretic Interpretation of Matroids?

Hello everyone! First time poster, long time lurker here. I have a really basic question that has been bugging me for sometime. Specifically, I'm not exactly sure what the 'correct' category ...

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**0**answers

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### Q-construction and Gabriel-Zisman Localization

It might be a stupid question.
When I took a look at the definition of Q-construction. It makes for an exact category $P$, one defines a new category $QP$ whose objects are the same as $P$ but ...

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**0**answers

623 views

### What are the relationship between various definitions for quasi coherent sheaves?

It seems that there are many definitions of quasi coherent sheaves(modules). There is a nice page on nLab quasi coherent sheaves
My questions are:
Are there any other definitions of quasi coherent ...

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**1**answer

971 views

### What is a proper stack?

I have seen the use of the word "proper Deligne-Mumford stack". Now, it is clear to me what it means for a morphism f of stacks to be proper: as usual it should be representable, and every morphism ...

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**3**answers

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### When is a classification problem “wild”?

I hope someone can point me to a quick definition of the following terminology.
I keep coming across wild and tame in the context of classification problems, often adorned with quotes, leading me to ...

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**25**answers

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### What are the most misleading alternate definitions in taught mathematics?

I suppose this question can be interpreted in two ways. It is often the case that two or more equivalent (but not necessarily semantically equivalent) definitions of the same idea/object are used in ...

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**2**answers

307 views

### Definition modifications without choice

What definitions or equivalencies between definitions for standard set theory objects (such as large cardinals) do not hold or do not carry through in the expected manner to the world without choice? ...