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3h
comment Is it possible to delete undesired identifications in algebraic structures?
If all you want to do is to factorise morphisms as monomorphisms followed by epimorphisms, or something like that, then you can look at the cograph factorisation $X \to X + Y \to Y$. The second half is always a split epimorphism, and the first half is a monomorphism in many interesting cases, e.g. in pointed categories.
16h
comment Image is not a manifold when considered as a subset: how is this possible?
For instance, consider a self-intersecting regular curve.
2d
comment Full stop as mutiplication sign
To say nothing of the Europeans who use a comma for the decimal point...!
2d
comment Lifting a homotopy class $S^k\to X$ into a simplicial set $X$ which is not fibrant but satisfies some weaker horn filling condition
What is $S^k$? Do you mean $\partial \Delta^{k+1}$?
Aug
30
comment Existence of tensor product via category theory
That result is more or less irrelevant. What you need is an adjoint functor theorem.
Aug
30
comment How to recover multiplication of group elements from category of groups?
The question could equally well be asked of the Lawvere theory of groups: given the Lawvere theory of groups as an abstract Lawvere theory, is there a way to recognise $(x, y) \mapsto x y$?
Aug
28
comment Is there a notation for “Bounded Kleene star”?
You could write $V^{\le n}$, perhaps. But you should explain it if you do.
Aug
28
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 $1 \mapsto y x$.
Aug
28
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.
Aug
28
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.
Aug
28
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.
Aug
28
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 $\mathbf{Set}$.
Aug
27
comment Simple question about closed immersions
Yes, that's right.
Aug
26
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.
Aug
26
comment What is the “internal language of a topos”?
Yes. Of course, Grothendieck toposes are elementary toposes too.
Aug
26
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.
Aug
26
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!