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Dec
20
comment Is $(gf)(X) = g ( f(X))$ in a category?
Images are in general not useful without some structure on the ambient category. If $\mathcal{C}$ has pullbacks, then images behave sufficiently well that they compose as you expect.
Dec
19
comment Difference between a stalk of a sheaf and a fiber of a vector bundle
That is precisely the sense I mean. A pullback is a limit.
Dec
19
comment Why surjectivity stable under base change?
You need the following fact: if $K \to L$ and $K \to L'$ are a pair of field extensions, then there is a field $M$ and a pair of field homomorphisms $L \to M, L' \to M$ making the obvious diagram commute.
Dec
19
revised Difference between a stalk of a sheaf and a fiber of a vector bundle
added 453 characters in body
Dec
19
answered Difference between a stalk of a sheaf and a fiber of a vector bundle
Dec
19
comment Examples of fields of characteristic 1
Most likely the downvote was for the suggestion that $\{ 0 \}$ is a field...
Dec
19
comment Clarifications about the definition of algebraic systems and algebraic structures
Hmmm. I think by ‘algebraic structure’ most people mean a set with operations but no relations.
Dec
19
comment Clarifications about the definition of algebraic systems and algebraic structures
Your definitions are rather vague. Can you give exact quotations?
Dec
19
accepted Automorphism extension property of Galois extensions
Dec
19
comment What guarantees that non-geometric definition of trigonometry is actually the same as the geometric definition?
The standard definition of $\pi$ in analysis is "the first positive zero of $\sin$", so it's automatic there as well.
Dec
18
comment What is wrong with my proof? Every extension is separable? (of course not)
What if $p'$ is the zero polynomial?
Dec
18
comment Definition of differential of map (in algebraic geometry)
One doesn't usually have a cotangent bundle so much as a cotangent sheaf, in which case it is not appropriate to use fibre product notation for pullback.
Dec
18
comment Hartshorne Exercise II. 3.19 (b)
If you want a hint instead of a complete solution, then say so in your question. Otherwise this is a perfectly valid answer.
Dec
17
comment Terminology Question: “G Acts on itself by Right Multiplication”
The second is what is meant: this is the regular right $G$-action on itself.
Dec
17
comment Non-concrete non-set theoretic things
Properly defined it isn't a quotient – it's a localisation.
Dec
16
answered Does such a natural number exist, that it would be divisible by every other natural number
Dec
16
comment Does such a natural number exist, that it would be divisible by every other natural number
Depends on your definition. I say $x \mid y$ if and only if $\exists z . y = x z$, in which case $x \mid x$ always.
Dec
16
comment Automorphism extension property of Galois extensions
Ah, so it doesn't so much follow from the finite case as it does have the same proof. Pity, I was hoping it was just abstract nonsense...
Dec
16
asked Automorphism extension property of Galois extensions
Dec
16
comment Why don't we define “imaginary” numbers for every “impossibility”?
@Arafinwe So, are you saying $0 = 1$ is an acceptable state of affairs?