Mariano Suárez-Alvarez
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2d
comment intersection of all $2$-sylow in $S_n$
Well, do you know of any normal subgroup of $S_n$?
2d
comment Non-zero maps between modules
Please oh please oh please oh please try to look for examples of things.
2d
answered Non-zero maps between modules
2d
comment Why associativity $h \circ (g \circ f) = (h \circ g) \circ f$ is required in composition?
Useful definitions capture the useful traits of useful objects. One does not make random definitions.
2d
comment Why associativity $h \circ (g \circ f) = (h \circ g) \circ f$ is required in composition?
Your question is backwards, really. Category theory defines categories to model objects that pre-existed the creation of category theory, abstracting a few of their useful properties. Among those properties is that of associativity.
2d
revised Why associativity $h \circ (g \circ f) = (h \circ g) \circ f$ is required in composition?
deleted 1 character in body
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answered Why associativity $h \circ (g \circ f) = (h \circ g) \circ f$ is required in composition?
2d
comment Conjugacy Classes of a group G - Intuitive Understanding
I suggest you search a bit the site, since this has already been asked.
2d
comment Is integration of $x\operatorname{cosec}(x)$ defined?
I am using comments for one of its intended purposes: to signal an error.
2d
comment Is integration of $x\operatorname{cosec}(x)$ defined?
There is a difference between making a discussion complicated and asserting what is a false statement under the usual definitions of the terms involved. You could expand a bit in what exactly is meant by «integrability in elementary terms» as opposed to good ol' «intregrability». As it stands, I am afraid this is more confusing than helpful.
2d
comment Is integration of $x\operatorname{cosec}(x)$ defined?
What you found is a «closed form» only because you defined it to be. Te polylogarithm function is defined (amng other ways) as an integral. You could decide that the integral the OP wants defines the Patel function and call that a closed form, too...
2d
comment Is integration of $x\operatorname{cosec}(x)$ defined?
Well, it is not «non-integrable»...
2d
comment Research in Non Commutative geometry
The area is very active. «The entire mathematical community» is such a tenuous concept that what interests it is quite irrelevant. I suggest you stop paying attention to whatever ranking it is you are looking at.
2d
comment Why are compact complex manifolds Liouville?
It is not true that if $f:X\to\mathbb C$ is holomorphic then $f$ is open. This is only true if the function is non-constant, and you cannot put the hypthesis in a parenthetical remark!
2d
comment Why are compact complex manifolds Liouville?
In the $C^\infty$ category, there is not much difference between a vector bundle and its dual, but in the algebraic/holomophic categories there is a world of difference. You should try to compute sections by hand on the tangent bundle on $P^1$ and its dual before continuing to read whatever paper it is you are reading.
2d
comment Why are compact complex manifolds Liouville?
But that happens very very often, in fact! Just consider the canonical bundle on projective space and its dual. The computation is done in Hartshorne and many other places.
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comment Why are compact complex manifolds Liouville?
For the second question, the answer is also yes, and this follows immediately from exactly the same argument.
2d
comment Map between $SO(n)$ is homotopic to the identity?
SO(2) is a circle... Try to do a picture!
Jul
3
comment Why is the sheaf $\mathcal{O}_X(n)$ called the “twisting sheaf” (where $X=\operatorname{Proj}(S)$ for a graded ring $S$)?
Because the $O(1)$ of $P^1$ is morally a Möbius band, I imagine.
Jul
2
comment Ring Structure for Non Commutative Groups: Is there a grander reason for Abelian requirements?
«All groups of order up to $6$» is an almost negligible amount of evidence!