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Jan
29
revised Interesting sites without pull-backs
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Jan
29
comment Interesting sites without pull-backs
"Also, you don't need pullbacks in order to use the usual definition of a sheaf: it suffices to show that pullbacks (i.e., base changes) of covering families exists and are covering families. " ---- That's a good point. This is what I actually had in mind when writing the question, though I carelessly stated it in terms of the category itself having pull-backs. I will edit the question accordingly.
Jan
27
asked Interesting sites without pull-backs
Dec
29
accepted Under what conditions is the exponential map on a Lie algebra injective?
Dec
3
accepted Mathematical significance of the “Dirac conjugate”
Nov
8
answered Compactification: density of a uniform space $X$ in the spectrum of $UC^b(X)$
Oct
24
awarded  Notable Question
Oct
21
asked Why do we represent groups in the category of vector spaces?
Sep
21
comment Question on unitary representation of non-compact simple Lie groups
If the center of $G$ is finite, then your same argument should yield a finite covering map $G\rightarrow SU(n)$ with image a subgroup $H$ of $SU(n)$. Finite covering maps are closed, and so $H$ should be closed, hence compact. We then have an isomorphism $G/\operatorname{Ker}(\rho )\rightarrow H$, $\rho :G\rightarrow SU(n)$ the representation. As the quotient of a noncompact group $G$ by a finite group $\operatorname{Ker}(\rho )$ cannot be compact, this is a contradiction.
Sep
16
awarded  Civic Duty
Sep
11
accepted Are adjunctions unique?
Sep
11
comment Are adjunctions unique?
Ahhh, okay. I had to write more details down to see what you meant, but now I see how it follows. Thanks!
Sep
10
revised Are adjunctions unique?
added 12 characters in body
Sep
10
comment Are adjunctions unique?
Okay, I like this. I have updated the question accordingly. You might then rephrase the question as "Is information lost in passing from the adjoint pair (i.e. with the data of the particular adjunction included) to the adjointable pair?" If the adjunction itself were unique, then you could recover it from just $F$ and $G$ alone.
Sep
10
comment Are adjunctions unique?
What? I don't mean to ask whether the functors are unique, I mean to ask whether the adjunction that relates them is unique. Does uniqueness of the functors imply uniqueness of the natural isomorphism $\Phi _{X,Y}$? If so, I do not see it . . .
Sep
10
comment Are adjunctions unique?
What do you mean? I agree that the thing that matters is the the functors together with the adjunction, but I specifically needed a term that 'forgot' about any specific adjunction so as to be able to actually ask the question (at least in the first way that came to mind).
Sep
10
asked Are adjunctions unique?
Aug
12
asked Symmetry of the second derivative
Aug
11
comment The Fundamental Theorem of Calculus (for the lebesgue integral)
@Henry Yeah, that was a stupid mistake of mine. Sorry about that. It has been corrected.
Aug
11
revised The Fundamental Theorem of Calculus (for the lebesgue integral)
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