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Results tagged with soft-question
Search options questions only
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user 41291
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.
6
votes
2
answers
468
views
Is the logic of the ($\infty$-?)topos of simplicial sets "contradictory up to homotopy"?
In a sense this is a followup to my earlier question Does the (1-)topos structure on simplicial sets have any homotopy-theoretic significance?.
In the topos of simplicial sets, the subobject classifie …
- 21.3k
35
votes
12
answers
3k
views
No canonical isomorphism [duplicate]
I thought that it would be interesting to collect into a big list various instances of isomorphic structures with no preferred isomorphism between them. I expect the examples to be interesting since i …
- 18.4k
4
votes
0
answers
111
views
Is there a simple algebraic setup to accomodate fibres and cofibres at the same time?
If I understand it correctly, there are two mutually dual "leading principles" in homotopy theory:
never perform quotients, add structure instead;
never require subobjects, take fibres instead.
Al …
- 18.4k
18
votes
3
answers
7k
views
What is so special about set theory anyway? [closed]
(Later edit - tried to clarify a couple of vague places concerning interpretations of theories that became evident in comments (thanks to Andrej Bauer, Mauro ALLEGRANZA and Emil Jeřábek). (To closers …
- 18.4k
12
votes
1
answer
351
views
Multiplicative infinitesimals in q-analogs?
Risking to be downvoted, here is a very lightweight question.
In various fields - say, algebraic geometry, nonstandard analysis, synthetic differential geometry - infinitely small quantities, i. e. th …
CommunityBot
- 1
35
votes
1
answer
2k
views
Are there topological versions of the idea of divisor?
I am trying to extract a particular, more lightweight and more focussed at the same time, case of my recent question Which of the physics dualities are closest in essence to the Spanier-Whitehead dual …
- 6,813
7
votes
0
answers
234
views
$q$-crystals - is there such a thing?
There are several important facts that I first heard about here on MO. One of the most enlightening of these is that $\mathscr D$-modules on a scheme $X$ may be viewed as sheaves on the groupoid of in …
CommunityBot
- 1
0
votes
0
answers
415
views
Solving the equation $\operatorname{Powerset}(X)=\varnothing$
There are (at least) two variants of this question.
Is it possible to modify the axioms of set theory, without arriving at obvious contradiction, in such a way that in a model of the theory there is …
- 18.4k
13
votes
1
answer
577
views
Which nice/deep elaborations on the (operators <-> sheaves) / (endomorphisms <-> objects) th...
A linear operator $T:V\to V$ on a (say) vector space over a field $k$ is just a $k[T]$-module, and may be viewed as the sheaf $\mathscr F_T$ over $\mathbb A^1_k$, with fibre over $\lambda\in k$ equal …
CommunityBot
- 1