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- 0 posts edited
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- 183 votes cast
Mar
12 |
comment |
Which conjectures are proved for sofic groups?
I would add to the list Gottschalk's conjecture (in a very general version) by Gromov (who defined sofic groups) |
Mar
6 |
comment |
Analogy between Lagrange's Theorem and Rank-Nullity Theorem?
You are right, let's say that I view an analogy between the two things as long as Lagrange's Theorem is applied to a quotient over a normal subgroup. It is in fact true that the general statement is more subtle, but this difference has no analogy in the category of vector spaces (nor in any abelian category, where every subobject is the kernel of some morphism). |
Feb
23 |
awarded | Custodian |
Feb
23 |
reviewed | No Action Needed Centralizer of a dense subgroup in a maximal subgroup of a reductive group |
Feb
17 |
revised |
Square of non-zero element in group algebra is always non-zero?
added 134 characters in body |
Feb
17 |
comment |
Square of non-zero element in group algebra is always non-zero?
sorry, didn't see that! |
Feb
17 |
answered | Square of non-zero element in group algebra is always non-zero? |
Sep
1 |
comment |
Ring epimorphisms, and epimorphism in the category of small preadditive cats
@MartinBrandenburg, I do not understand your comment. The functor $\Phi$ is clearly defined as the restriction of $\phi_!$. Then $\Phi^*$ is defined sending a functor $F:\mathrm{mod}(S)^{op}\to \mathrm{Ab}$ to $F\circ \Phi$. Finally $\Phi_!$ is the additive left Kan extension along $\Phi$, you can construct it "explicitly" using tensor product of bifunctors. |
Jul
22 |
comment |
Ring epimorphisms, and epimorphism in the category of small preadditive cats
@JeremyRickard, Thanks for your comments! Since there is a bounty ending tomorrow, if you want to post your partial answer with some details, I will accept it before tomorrow. Then it will be possible to edit. Also, I think that to have this partial answer could help others to give a complete answer. |
Jul
21 |
comment |
Ring epimorphisms, and epimorphism in the category of small preadditive cats
So you are asking whether $\Phi$ in my question is surjective on objects, provided $\phi$ is an epimorphism. I do not know if this is true but I do not see any easy counterexample right now. |
Jul
14 |
asked | Ring epimorphisms, and epimorphism in the category of small preadditive cats |
Jul
10 |
answered | Spliting of short exact exact sequences of partially ordered groups |
Jul
8 |
comment |
Spliting of short exact exact sequences of partially ordered groups
Also, are you considering just Abelian groups, or arbitrary group? |
Jul
8 |
comment |
Spliting of short exact exact sequences of partially ordered groups
It depends what you actually want. In Abelian categories, the fact of having a $\gamma$ which is right inverse to $\beta$, tells you that $G=H\oplus G/H$. On the other hand, in general categories that condition just tells you that $G/H$ is a retract of $G$, but not a summand. Of course, in any case, you want $\gamma$ to be a morphism in your category, so in this case you want it to be an order homomorphism but, the mere existence of such $\gamma$ may not imply the splitting. |
Jul
4 |
awarded | Yearling |
Mar
16 |
awarded | Enlightened |
Mar
16 |
awarded | Nice Answer |
Mar
16 |
answered | Regarding the definition of S-flows over a category (given a monoid S) |
Mar
12 |
comment |
Lattice of subobjects of a particular coproduct
oh, you are right, if you want to post it as an answer I'd be happy to accept it. |
Mar
12 |
comment |
Lattice of subobjects of a particular coproduct
Sorry, I wanted to say by an automorphism of the ring. I mean, let $\phi:R\to R$ be an automorphism. Using $\phi$ you can see $R$ as an $R-R$-bimodule (differently than in the standard way) and you can tensor by that bimodule. |