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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.