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Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
4
votes
What do people mean by "subcategory"?
Do people tend to mean the official
definition?
I think "official" belongs in scare-quotes... I tend to think that "subcategory" is an evil notion. I'm not published anywhere, but in my notes …
3
votes
Theorems for nothing (and the proofs for free)
Oh! From uniqueness of the countable dense linear order without endpoints: take (for instance) a countable ordinal $\lambda$, and consider the anti-lex order on $\mathbb{Q}\times\lambda$. This is a c …
5
votes
Why should I prefer bundles to (surjective) submersions?
This is probably making a hash of the earlier answers, but bundles are special fibrations; specifically, they are fibrations with (not canonically) isomorphic fibers. And we all like fibrations, righ …