The tag has no wiki summary.

learn more… | top users | synonyms

3
votes
5answers
347 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 ...
32
votes
2answers
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 ...
4
votes
0answers
277 views

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 ...
9
votes
0answers
610 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 ...
4
votes
1answer
896 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 ...
18
votes
3answers
2k views

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 ...
61
votes
23answers
22k views

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 ...
3
votes
2answers
302 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? ...