1
vote
1answer
48 views

What is the cokernel of $\Bbb Q^{\text{disc}} \hookrightarrow \Bbb R$?

These two should be the standard examples for why Locally compact abelian groups are not an abelian categoty. The cokernel of any of these maps should is not a LCAG. $$\Bbb Q^{\text{disc}} ...
2
votes
1answer
46 views

Familiarizing with the Grothendieck topos $\mathbf{B}G$.

I am trying to familiarize with the Grothendieck topos $\mathbf{B}G$ of continuous $G$-sets, where $G$ is a topological group. I am unfortunately not very familiar with working with different ...
3
votes
2answers
139 views

Is Hom$(G,-)$ left exact if morphisms are required to be continuous?

Suppose now that the objects in question are abelian topological groups $G$ so that morphisms are continuous group homomorphisms. Given an exact sequence of abelian topological groups $0 \to G''\to G ...
3
votes
0answers
97 views

Does 'much' of what is known about groups carry over to groupoids? [closed]

Lawvere & Rosebrugh remark in Sets for Mathematics (2003) that much of what is known about groups carries over to groupoids. But this seems contradicted by statements in M Grandis' Directed ...
8
votes
2answers
375 views

Exact sequence in a nonabelian category [previously: “Exact sequence for topological groups?”]

If $A$, $B$, and $C$ are topological groups, and $f: A \to B$ and $g: B \to C$ are two continuous group homomorphisms, what does it usually mean for $$1 \to A \stackrel{f}{\to} B \stackrel{g}{\to} C ...
13
votes
2answers
716 views

what are the product and coproduct in the category of topological groups

I know the limits in the categories of groups, abelian groups and topological spaces and was wondering about the same thing.