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 Revival
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4h
comment Is there a notation for “Bounded Kleene star”?
You could write $V^{\le n}$, perhaps. But you should explain it if you do.
5h
comment How to recover multiplication of group elements from category of groups?
I don't think it is possible to distinguish $1 \mapsto x y$ from $1 \mapsto y x$.
5h
comment If $M$and $N$ are R- modules, then under what conditions $\operatorname{Hom}(M,N)$ the space of R-module morphisms from M to N, is projective?
Here's something that is true, which you might like to prove: $\mathrm{Hom} (M, N)$ is projective if M is finitely generated projective and N is projective.
14h
comment I need the paper “ J. Zhang, A note on finite groups satisfying the permutizer condition, Sci. Bull. 31 (1986) 363–365”
You will probably have to go to a library and look in the archives.
14h
comment I need the paper “ J. Zhang, A note on finite groups satisfying the permutizer condition, Sci. Bull. 31 (1986) 363–365”
Here is the MathReview. It appears to have been published in China.
15h
comment generalized affine scheme
That diagram is very important. Since $\bar{R}$ is left exact, coequalisers in $\mathbf{FPAlg}_k^\mathrm{op}$ are sent to equalisers in $\mathbf{Set}$.
1d
comment Simple question about closed immersions
Yes, that's right.
2d
comment Is it true that $A \in A$?
Errors like these are often caused by using $\cdots$ (or $\vdots$) without thinking about what it really means.
2d
awarded  Revival
2d
comment What is the “internal language of a topos”?
Yes. Of course, Grothendieck toposes are elementary toposes too.
2d
comment generalized affine scheme
Sure. But that's not really the point. Forget about algebraic theories for the time being. What you are asking for is a left exact functor $\bar{R} : \mathbf{FPAlg}_k^\mathrm{op} \to \mathbf{Set}$ such that $\bar{R} (k [X_1, \ldots, X_n]) = k^n$ in a canonical way – there is really only one way of doing this.
2d
revised generalized affine scheme
edited tags
2d
comment generalized affine scheme
Can you do this if you use the standard definitions of field/ring/etc.?
Aug
25
comment Is the set containing just zero a mathematical field?
@GregoryGrant I have never encountered a book that says $0 \ne 1$ for a ring. For integral domains and fields, sure.
Aug
25
comment When does Sheafification commute with direct image?
There are already counterexamples to your suggestions in the answer.
Aug
24
comment Question about “immediate” observation about finitely presentable objects
The quotient of a congruence is literally a quotient in the classical sense, and the kernel pair of any homomorphism is a congruence. So the coequaliser has to be the quotient by the smallest congruence. Think concretely!
Aug
24
comment How to give “categorical” specifications of categories like Grp?
Yes, but that doesn't preclude stupid descriptions, e.g. a generators-and-relations presentation...
Aug
24
revised When does Sheafification commute with direct image?
edited tags
Aug
24
answered When does Sheafification commute with direct image?
Aug
24
comment Can we bypass connection?
Connections fail to be tensors because they measure the difference between a tensor and a non-tensor. So they are non-tensors by design.